Preheat the oven to 325 degrees F. Coat three 8-inch round cake pans and one 8-inch (1 1/2-quart) ovenproof bowl with cooking spray. Make the cake mixes as directed; pour 3 1/2 cups batter into the bowl and divide the rest among the cake pans.
Bake until a toothpick inserted into the cakes comes out clean, 20 to 25 minutes for the 8-inch cakes and about 45 minutes for the bowl cake. Let the cakes cool about 20 minutes, then turn out onto racks to cool completely.
Stack the three 8-inch cakes on a cardboard circle or cutting board, spreading frosting between each layer; put the top layer on upside down. Spread more frosting on the top layer.
Trim the larger side of the bowl cake with a long serrated knife to make it level, then place cut-side down on top of the layer cake.
Trim around the side of the layer cake so it is the same diameter as the bowl cake. Transfer the cake to a parchment-lined baking sheet; cover with a thin layer of frosting. Freeze 15 minutes.
Cover the cake with more frosting, then mark the top with a skewer to separate into three sections. Make stripes of yellow, blue and red coarse sugar on the top of the bowl cake.
Cut a 6-by-40-inch strip of parchment paper. Make small pleats in the parchment 1 to 1 1/2 inches apart.
Fold down one long edge of the paper by about 1/4 inch to make a rim; fold again to secure.
Wrap the paper around the cake with the folded edge on top, leaving the sugared part exposed. Gently press the paper against the frosting, then tuck the bottom edge of the paper under the cake using an offset spatula.
Photograph by Ralph Smith