The method is really simple, and pretty obvious from the pictures - check out the video at the above link for additional details.
Step 1: use a standard white cake mix, making sure you use only egg whites (no yellow).
Step 2: pour the batter into a number of cups. Add quite a bit of gel food coloring (like in the case below, probably 1/2 teaspoon, or ~ 2 ml) to make really saturated colors. Mix with plastic spoons, scraping sides (easier to clean up).
Step 3: Pour into each color in turn foil (prettier, more of a surprise) cupcake cups - the recipe for use made 16 cupcakes. You sort of have to use trial and error, but remember - all your colors should only fill the cup 60% of the way, so, think a dollop the size of a quarter or 50 cent piece.
Bake and eat. OK, if you want, frost to make it more of a surprise - white frosting is most spectacular.
Opening text
Just out of the oven:
In its full glory: