I've seen all different color icons. Blue, gold, red, etc. but where did the cake icons come from? Does it mean it's that persons Birthday?

they were recently released so everyone knows when your birthday is, you only get the icon once a year :D

Cool! Thanks, now I need to run off and buy a Birthday present for my friend!

, is there a way to suppress the cake icon?

As far as I know there is no way to do this yet.