Preheat oven according to cake mix directions. Generously grease and flour a 12-cup bundt pan; set aside.

Make cake batter as directed on box, using water, oil and egg whites. Pour 1 cup of the batter into a small bowl; stir in red food coloring until well mixed. Pour another cup of the batter into a separate bowl; stir in blue food color until well mixed.

Pour red cake batter into bottom of pan. Carefully pour the white batter over red batter in pan. Carefully pour blue batter over white batter. (The blue batter does not need to cover the white batter completely). When you add the batter to the pan, do not mix with a spoon. Just pour it in so the colors don't mix but rather, just rest on top of each other in the pan.

Bake as directed on box or until toothpick inserted near center comes out clean. Cool cake 10 minutes. Meanwhile, place cooling rack over cookie sheet. Turn pan upside down onto cooling rack. Cool cake completely, about 30-45 minutes. 

When cake is cool, divide the frosting evenly into 3 microwavable bowls. Microwave 1 bowl of frosting uncovered on HIGH a few seconds until smooth enough to drizzle over cake. With spoon, drizzle all of the 1st bowl of microwaved frosting all over the cake, back and forth around the cake in a striping pattern. Repeat microwaving second bowl of frosting until smooth. Stir in a few drops of the blue food coloring until well blended. Drizzle over cake, scattering back and forth. Repeat with remaining frosting and red food coloring, making sure red, white and blue can be seen on the cake. Sprinkle with red, white and blue sprinkles, if desired. Let cake stand at room temperature until frosting is set before serving.