Are you set on this cake?
If not my DD wanted a rainbow party for her 6th birthday and I made her a cake with the seven colours of the rainbow all mixed in together (so had a tie dye type effect), butter icing and then on the outside I had each colour of the rainbow in skittles going around the cake. Then on top I had a number 6 out of sprinkles
It looked fabulous!! And was so much easier than the layers cake.

Happy to show you photos if you like.

Good luck.