Addressing EACH of the 3x3x3 LEDs separately I read a few 3x3x3 LED tutorials, e.g. let us take this one:

http://www.instructables.com/id/Making-an-Arduino-3X3-LED-Cube-in-Less-Than-30-Min/?ALLSTEPS

As far as I understand, you can address any of the 3x3 light columns:

*  *  *       1  2  3
*  *  *       4  5  6
*  *  *       7  8  9


and each of the three vertical layers:

top
middle
bottom


But can I address each of the 27 leds separately? In other words, can I light up:

1+  2   3         bottom layer
4   5+  6
7   8   9

1   2+  3         middle layer
4+  5   6
7   8   9
No, the three transistors are there to select the layer you want to control. At every moment only ONE layer can be on. But if you switch through controlling these layers fast enough, you can create the illusion of having multiple leds on even across layers. THis is because the human eyes are just not capable of seeing lights flashing at a high rate.

TL;DR
No you can't address them individually, but you can create the illusion that you can.