Heat oven to 350 degrees F. Grease 10 x 2-inch round layer-cake pan.
Prepare batter according to package directions. Pour into pan.
Bake in 350 degree F oven 45 to 50 minutes, until wooden pick inserted in center comes out clean. Cool cake in pan on rack 5 minutes. Remove from pan to rack to cool completely.
Cut cake in half crosswise. Spread thin layer of frosting over bottom of one of the halves. Press halves together to make semicircle. Trim any uneven edges. From center of base of rainbow, cut semicircle, 2 inches high, 4 inches across at bottom. Position cake on serving tray or plate, cut side down.
Divide frosting into batches; tint with desired colors. Spread frosting over top curved surface of cake. Spoon tinted frostings into pastry bags fitted with round writing tips. Pipe colors, in rows, on side of cake, following curve of cake to simulate colors of rainbow.
Cut marshmallows in half horizontally. Attach together at sides with white frosting to form cloud clusters. Press against side of cake. Makes 10 servings.