Installing Ubuntu without DVD or Flash Drive
My objective is to post a procedure that would allow you to boot a Ubuntu Desktop Live. Once you have booted, you could then install the regular Ubuntu Desktop. The only way I can figure out how to boot Ubuntu Desktop Live is by using GRUB. The problem is I can not determine a way to install GRUB without first installing some version of Linux. In this case, I choose to install Ubuntu Server inside a VirtualBox machine. This machine was configured to use a subset of the Mac's physical HD partitions. Once GRUB was installing in these partitions, Ubuntu Desktop Live could boot without using VirtualBox.
Install Ubuntu Server

To start I will assume your current hard disk is configured as shown below.
/dev/disk0 (internal, physical):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        +80.5 GB    disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:                  Apple_HFS Macintosh HD            79.7 GB    disk0s2
   3:                 Apple_Boot                         650.0 MB   disk0s3

The command below will create approximately 40 GB of free space at the end of your internal disk. This command will automatically relocate the disk0s3 partition.
diskutil resizevolume disk0s2 40g

The results can be summarized by the output from the diskutil list command, shown below.
/dev/disk0 (internal, physical):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        +80.5 GB    disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:                  Apple_HFS Macintosh HD            40.0 GB    disk0s2
   3:                 Apple_Boot Recovery                650.0 MB   disk0s3


Before using VirtualBox, all new linux related partitions have to be created. I choose the third party tool gdisk to create the partitions. Below is a list of the partitions that need to be created.

1.9 GB partition to hold the contents of the Ubuntu Desktop Live iso. This will allow you to replace Ubuntu Server with Ubuntu Desktop.
1 MiB Bios Boot Partition to hold GRUB boot code.
4 GiB Linux Swap Partition. This was chosen to be the same size as your RAM.
The remaining space to be allocated for Ubuntu files.

The output from using the gdisk /dev/disk0 command to edit the GPT is given below.
GPT fdisk (gdisk) version 1.0.3

Warning: Devices opened with shared lock will not have their
partition table automatically reloaded!
Partition table scan:
  MBR: protective
  BSD: not present
  APM: not present
  GPT: present

Found valid GPT with protective MBR; using GPT.

Command (? for help): p
Disk /dev/disk0: 157286400 sectors, 75.0 GiB
Sector size (logical): 512 bytes
Disk identifier (GUID): A7A204BD-463D-4EE5-9A78-8E9804D1539F
Partition table holds up to 128 entries
Main partition table begins at sector 2 and ends at sector 33
First usable sector is 34, last usable sector is 157286366
Partitions will be aligned on 8-sector boundaries
Total free space is 77482197 sectors (36.9 GiB)

Number  Start (sector)    End (sector)  Size       Code  Name
   1              40          409639   200.0 MiB   EF00  EFI System Partition
   2          409640        78534639   37.3 GiB    AF00  Macintosh HD
   3        78534640        79804175   619.9 MiB   AB00  Recovery HD

Command (? for help): n
Partition number (4-128, default 4): 
First sector (34-157286366, default = 79804176) or {+-}size{KMGTP}: 
Last sector (79804176-157286366, default = 157286366) or {+-}size{KMGTP}: +1900M
Current type is 'Apple HFS/HFS+'
Hex code or GUID (L to show codes, Enter = AF00): 8300
Changed type of partition to 'Linux filesystem'

Command (? for help): n
Partition number (5-128, default 5): 
First sector (34-157286366, default = 83695376) or {+-}size{KMGTP}: 
Last sector (83695376-157286366, default = 157286366) or {+-}size{KMGTP}: +1M
Current type is 'Apple HFS/HFS+'
Hex code or GUID (L to show codes, Enter = AF00): ef02
Changed type of partition to 'BIOS boot partition'

Command (? for help): n
Partition number (6-128, default 6): 
First sector (34-157286366, default = 83697424) or {+-}size{KMGTP}: 
Last sector (83697424-157286366, default = 157286366) or {+-}size{KMGTP}: +4G
Current type is 'Apple HFS/HFS+'
Hex code or GUID (L to show codes, Enter = AF00): 8200
Changed type of partition to 'Linux swap'

Command (? for help): n
Partition number (7-128, default 7): 
First sector (34-157286366, default = 92086032) or {+-}size{KMGTP}: 
Last sector (92086032-157286366, default = 157286366) or {+-}size{KMGTP}: 
Current type is 'Apple HFS/HFS+'
Hex code or GUID (L to show codes, Enter = AF00): 8300
Changed type of partition to 'Linux filesystem'

Command (? for help): p
Disk /dev/disk0: 157286400 sectors, 75.0 GiB
Sector size (logical): 512 bytes
Disk identifier (GUID): A7A204BD-463D-4EE5-9A78-8E9804D1539F
Partition table holds up to 128 entries
Main partition table begins at sector 2 and ends at sector 33
First usable sector is 34, last usable sector is 157286366
Partitions will be aligned on 8-sector boundaries
Total free space is 6 sectors (3.0 KiB)

Number  Start (sector)    End (sector)  Size       Code  Name
   1              40          409639   200.0 MiB   EF00  EFI System Partition
   2          409640        78534639   37.3 GiB    AF00  Macintosh HD
   3        78534640        79804175   619.9 MiB   AB00  Recovery HD
   4        79804176        83695375   1.9 GiB     8300  Linux filesystem
   5        83695376        83697423   1024.0 KiB  EF02  BIOS boot partition
   6        83697424        92086031   4.0 GiB     8200  Linux swap
   7        92086032       157286366   31.1 GiB    8300  Linux filesystem

Command (? for help): w

Final checks complete. About to write GPT data. THIS WILL OVERWRITE EXISTING
PARTITIONS!!

Do you want to proceed? (Y/N): y
OK; writing new GUID partition table (GPT) to /dev/disk0.
Warning: Devices opened with shared lock will not have their
partition table automatically reloaded!
Warning: The kernel may continue to use old or deleted partitions.
You should reboot or remove the drive.
The operation has completed successfully.


Note:  It would be a good idea to restart the Mac.

The output from the command diskutil list is shown below. This includes the new partitions created by using gdisk.
/dev/disk0 (internal, physical):
   #:                       TYPE NAME                    SIZE       IDENTIFIER
   0:      GUID_partition_scheme                        +80.5 GB    disk0
   1:                        EFI EFI                     209.7 MB   disk0s1
   2:                  Apple_HFS Macintosh HD            40.0 GB    disk0s2
   3:                 Apple_Boot Recovery                650.0 MB   disk0s3
   4:           Linux Filesystem                         2.0 GB     disk0s4
   5:        Bios Boot Partition                         1.0 MB     disk0s5
   6:                 Linux Swap                         4.3 GB     disk0s6
   7:           Linux Filesystem                         33.4 GB    disk0s7


Create folder named &quot;VirtualBox&quot; in your Documents folder.

Note: At this point, one should realize it would be easier to copy the commands from this document and paste them into the Terminal application window.


This step will create the files needed by VirtualBox to access the
physical partition where you will install Ubuntu. In a Terminal
application window, enter the following commands.
cd  ~/documents/virtualbox
sudo  chmod  go+rw  /dev/disk0s4
sudo  chmod  go+rw  /dev/disk0s5
sudo  chmod  go+rw  /dev/disk0s6
sudo  chmod  go+rw  /dev/disk0s7
sudo  vboxmanage  internalcommands  createrawvmdk  -filename  &quot;$PWD/linux.vmdk&quot;  -rawdisk  /dev/disk0  -partitions  4,5,6,7
sudo  chown  $USER  linux*.vmdk


Note: This access granted by the chmod command will only last
until OS X is rebooted.

The result should be the creation of the files linux.vmdk and
linux-pt.vmdk in your &quot;VirtualBox&quot; folder. Later, you will
select the file linux.vmdk to give a virtual machine access to
the physical partitions.

Configure the virtual machine. Open the VirtualBox application and
click on icon above the New label. Enter or select the values shown
below, then click the &quot;Continue&quot; button.

Use the default settings except for the hard drive. Choose the &quot;Use an existing virtual hard drive file&quot; button. Navigate to your &quot;VirtualBox&quot; folder. Highlight the linux.vmdk file. Open the linux.vmdk file. Your window should appear similar to what is shown below.

Click the &quot;Create&quot; button.
After returning to the VirtualBox application's &quot;Oracle VM VirtualBox Manager&quot; window, click on the icon above the &quot;Settings&quot; label. Next, click on the icon above the &quot;Storage&quot; label. Highlight &quot;Controller: SATA&quot; in &quot;Storage Devices&quot;, then select the &quot;Use Host I/O Cache&quot; option. Your window should appear similar to what is shown below.

Highlight the Empty CD/DVD and select &quot;Choose Virtual Optical Disk
File...&quot; to attach the &quot;ubuntu-16.04.3-server-amd64.iso&quot; file. (Hint: Look for the
CD/DVD icons)

Click OK to close the window. Your &quot;Oracle VM VirtualBox Manager&quot;
window should appear similar to what is shown below.


Click on the icon above the &quot;Start&quot; label to boot from the &quot;ubuntu-16.04.3-server-amd64.iso&quot; file. You can proceed with the installation by choosing the default values until you reach the image shown below. Here, you should choose &quot;Manual&quot;.

Select #6, as shown below.

Select &quot;Use as:&quot;, as shown below.

Select &quot;swap area&quot;, as shown below.

Select &quot;Done setting up the partition&quot;, as show below.

Select #7, as shown below.

Select &quot;Use as:&quot;, as shown below.

Select &quot;Ext4 journaling file system&quot;, as shown below.

Select &quot;Mount point:&quot;, as shown below.

Select &quot;/ - the root file system&quot;, as shown below.

Select &quot;Done setting up the partition&quot;, as show below.

Select &quot;Finish partitioning and write changes to disk&quot;, as shown below.

Select &quot;Yes&quot;, as shown below.


When prompted to &quot;Install the GRUB boot loader to the master boot record?&quot;, select &quot;Yes&quot;, as shown below.

The install should proceed to completion.


Use Ubuntu Server to Setup Ubuntu Desktop Live

Using VirtualBox, boot to Ubuntu Server.

After logging in, enter the command below. This will give you root user privileges.
sudo  bash


Copy the MBR to an unused sector in the BIOS boot partition.
dd  if=/dev/sda  count=1  seek=1800  of=/dev/sda5


Insert ubuntu-16.04.3-desktop-amd64.iso into the virtual DVD drive.

Enter the commands given below to copy the files from the iso to the hard disk.

Note: The rsync command may take a while to complete.

mkfs.ext4  /dev/sda4
mkdir  live
mount  /dev/sda4  live
mkdir  dvd
mount  /dev/sr0 dvd
rsync  -a  dvd/*  live
eject
rmdir  dvd
umount  live
rmdir  live


Configure GRUB. Start by entering the following commands to edit the 40_custom file.
cd  /etc/grub.d
nano  40_custom

Add the following lines to the end of the 40_custom file. This will create Ubuntu Desktop Live and Installation entries in the GRUB menu.
menuentry &quot;Ubuntu Desktop 16.04.3 Live&quot; {
        set root=(hd0,4)
        linux /casper/vmlinuz.efi boot=casper ignore_uuid
        initrd /casper/initrd.lz
}
menuentry &quot;Install Ubuntu Desktop 16.04.3&quot; {
        set root=(hd0,4)
        linux /casper/vmlinuz.efi boot=casper only-ubiquity ignore_uuid
        initrd /casper/initrd.lz
}

After saving your changes to the 40_custom file, enter the following commands to edit the grub file.
cd  /etc/default
nano  grub

Find the following line in the grub file.
GRUB_DEFAULT=0

Change the line to appear as shown below.
GRUB_DEFAULT=3

Find the following line in the grub file.
GRUB_TIMEOUT=2

Change the line to appear as shown below.
GRUB_TIMEOUT=-1

After saving your changes to the grub file, use the following commands to update grub and return to your home directory.
update-grub
cd  ~


Exit being the root user and shutdown the virtual machine.
exit
shutdown  now



Use OS X to Setup Ubuntu Desktop Live

Copy the MBR GRUB boot code from the BIOS boot partition to the MBR.
cd  ~
sudo  dd  if=/dev/disk0s5  count=1  skip=1800  of=mbr.binary
sudo  fdisk  -u  -y  -f  mbr.binary  /dev/disk0
sudo  rm  mbr.binary


Convert to a Hybrid MBR/GPT scheme. The only reason for this step is to get around a bug in the Mac logic board BIOS firmware. Basically, the BIOS will not load the MBR into RAM unless there is an active partition in the MBR table. This conversion can be easily accomplished through the use of the interactive command shown below.
sudo  gdisk  /dev/disk0

The output from using this command is shown below.
GPT fdisk (gdisk) version 1.0.3

Warning: Devices opened with shared lock will not have their
partition table automatically reloaded!
Partition table scan:
  MBR: protective
  BSD: not present
  APM: not present
  GPT: present

Found valid GPT with protective MBR; using GPT.

Command (? for help): r

Recovery/transformation command (? for help): h

WARNING! Hybrid MBRs are flaky and dangerous! If you decide not to use one,
just hit the Enter key at the below prompt and your MBR partition table will
be untouched.

Type from one to three GPT partition numbers, separated by spaces, to be
added to the hybrid MBR, in sequence: 2 3 4
Place EFI GPT (0xEE) partition first in MBR (good for GRUB)? (Y/N): y

Creating entry for GPT partition #2 (MBR partition #2)
Enter an MBR hex code (default AF): af
Set the bootable flag? (Y/N): n

Creating entry for GPT partition #3 (MBR partition #3)
Enter an MBR hex code (default AB): ab
Set the bootable flag? (Y/N): n

Creating entry for GPT partition #4 (MBR partition #4)
Enter an MBR hex code (default 83): 83
Set the bootable flag? (Y/N): y

Recovery/transformation command (? for help): w

Final checks complete. About to write GPT data. THIS WILL OVERWRITE EXISTING
PARTITIONS!!

Do you want to proceed? (Y/N): y
OK; writing new GUID partition table (GPT) to /dev/disk0.
Warning: Devices opened with shared lock will not have their
partition table automatically reloaded!
Warning: The kernel may continue to use old or deleted partitions.
You should reboot or remove the drive.
The operation has completed successfully.


Note: As the above message states, It would be a good idea to restart your Mac.


Use the bless command to set your Mac to BIOS boot.
sudo  bless  --device  /dev/disk0  --setBoot  --legacy



Replace Ubuntu Server with Ubuntu Desktop

After properly blessing your Mac, restart to boot GRUB. You should get an image similar to what is shown below. Select &quot;Install Ubuntu Desktop 16.04.3&quot;.


Install until the message shown below appears. Shortly, after this message is displayed, the window will be populated by partition information. This information will obscure this message.

The window, with the partition information, will appear similar to what is shown below.

This message is wrong. The message clearly says &quot;You will not be able to create, delete or resize partition on this disk.&quot; Well, this is exactly what we will be doing.

Delete the last 3 partitions. Select a partition, then select the - character. Repeat for the two remaining partitions. The result should appear similar to what is shown below.


Add back the desired partitions, I choose the same as was deleted. You may want something different. Perhaps a LVM?
Select the free space as shown below, then select the + character.

Set the popup window as shown below, then select &quot;OK&quot;.

Select the free space as shown below, then select the + character.

Set the popup window as shown below, then select &quot;OK&quot;.

Select the free space as shown below, then select the + character.

Set the &quot;Mount point&quot; in the popup window, as shown below, then select &quot;OK&quot;.

Note: Do not change the &quot;Size:&quot; value. Your value may be different from what is shown below.


The final results are shown below. To proceed with the installation, select &quot;Install Now&quot;.


Select &quot;Continue&quot;. Let the installation proceed to conclusion.



Where to Next?
To boot back to OS X, you need to hold down the option key at startup.
You will probably want to use rEFInd as your boot manager.
I made the swap space 4 GiB, because I read this is the amount of RAM installed. Upon review, I see only 3 GiB is usable. A little extra swap space probably is nothing to be concerned over. If you wish, you could make adjustments to my posted installation procedures.
References
There is no reason for readers to look up any of these references. They appear here for my use.
GNU GRUB Manual 2.02
Creating a BIOS/GPT and UEFI/GPT Grub-bootable Linux system
How do I set the grub timeout and the grub default boot entry?
Installation/FromLinux
Can I boot a Live USB fully to RAM, allowing me to remove the disk?
How to bypass “Try it / Install” screen when booting from USB Live Session? (without installing in the USB)