Using pound-cake variation on side of box (add instant pudding and 1 extra egg), prepare cake mix according to package directions and bake in a 9 x 13-inch pan. Let cool completely.
Cut five 5-3/4-inch diameter circles and five 4-1/4-inch circles from paper. Place larger circles of paper on cake to form ring pattern. Using a serrated knife, cut out cake around pattern.
Place 1 cup frosting in bowl. Divide remaining frosting among 5 bowls, and tint one bowl black, one blue, one green, one red, and one yellow. Transfer tinted frostings to resealable plastic bags. Frost top of cake with white frosting.
Using the smaller circles of paper, score centers of rings on top of cake to create guidelines for using colored frostings. Snip corner from each bag of tinted frosting, and pipe rings on top of cake, following photo. Matching colors to rings on top, pipe frosting onto sides of cake, then smooth with a small spatula. Insert paper flags into cake.