An American cake for Fourth July red white and blue

This is a cake we tried (hey! we like to bake even if a bit early) from woman's world. It is beautiful.
2 packages (18.25 ounce each) white cake mix
6 egg whites
1/4 cup oil
1 package (.10 ounces) Duncane hines Frosting Creations cherry vanilla flavor mix
1 3/4 tsp no taste red concentrated food coloring
1/2 teaspoon royal blue concentrated food coloring
1 Tablespoon butter at room temperature
8 1/2 cups confectioners sugar from two one pound bags
1 Tablespoonclear if possible vanilla extract
1 (2.5 ounces) red, white and blue patriotic sprinkles
red and blue sprinkles

Position racks in upper and lower thirds of oven preheat to 350F
Coat 3 (9inch ) round cake pans with cooking sprays. Prepare cake mixes together with  2 2/3 cups water, egg whites and oil according to package directions, beating on medium high until smooth, 5-6 minutes.

Spread 2 1/4 cups batter in one round pan; reserve. Transfer 5 1/4 cups remaining batter to separate bowl; stir in cherry vanilla flavor mix. Spread 3 cups cherry batter in 13" by 9" inch pan; reserve. Stir red food coloring into remaining cherry batter; spread in another round pan. Stir blue food coloring  into remaining  plain batter, spread in remaining round pan. Bake 18-20 minutes  or until toothpick inserted to center comes out clean. Cool completely.

On medium high  speed, beat butter until light and fluffy, On low, gradually beat in sugar, then 1/4 cup water and vanilla until combined. On medium high , beat until fluffy, 8 minutes. Remove 1/4 cup frosting; cover and reserve.

Meanwhile, trim cake tops until level. Place blue cake layer on serving plate ; spread with one cup frosting. Top with white cake layer, spread with 1 cup frosting. Top with red cake layer . Spread remaining frosting over cake top and side.