Switch power ratings to control multiple RGB diodes
If you will have a current of 20mA (full brightness) per LED you can't use this switch. One switch has to deal with 120mA (6*20mA), which is more than twice of the allowed maximum. You can use bigger Resistors, to limit the current to ~8mA per LED if it isn't a problem for you to have them shine darker.
Otherwise you need a switch with a rating of atleast 120mA.

Fitting Resistors, calculated by 13.5V would be: