Preheat the oven to 350°F (175°C). Grease and flour three 8-inch round cake pans.

In a large mixing bowl, cream together the butter and sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition. Stir in the vanilla extract.

In another bowl, whisk together the flour and baking powder. Gradually add to the creamed mixture, alternating with milk.

Divide the batter into three bowls. Color one bowl with blue food coloring, one with red, and leave one plain (white).

Pour the blue batter into one prepared pan, the red batter into another, and the plain batter into the last.

Bake for 25-30 minutes or until a toothpick inserted in the center comes out clean. Let cool in pans for 10 minutes before transferring to wire racks.

In a large bowl, beat the softened butter until creamy. Gradually add powdered sugar, mixing until smooth.

Add vanilla extract and milk, and beat until fluffy. Divide the frosting into three bowls.

Color one bowl of frosting red and one blue, leaving one white.

Place the white cake layer on a serving plate. Spread a layer of white frosting on top.

Add the red layer on top and frost with red frosting. Top with the blue layer and frost the entire cake with white frosting.

Decorate the top with red and blue frosting, and sprinkle with white sprinkles to finish.