How to grant database creation privilege to a user in MySQL
ALL privileges includes "ALL" of them except "wITH GRANT OPTION"... Thus above command will let admin user create the database too.

You might want to show the error that you're getting. Note that in above GRANT you have not specified the password for admin user too.

Update:

You should be able to do following:

login as root and create user:

$] mysql -uroot -p
mysql&gt; grant all privileges on *.* to 'admin'@'localhost';


login as admin (without password):

$] mysql -uadmin -p
mysql&gt; create database admin;


When you login, you can verify your privileges as follows:

mysql&gt; show grants; 

or

mysql&gt; show grants for current_user();

mysql&gt; select current_user() will show you, user you logged in as.