Preheat oven to 350°F (175°C) and grease three round cake pans.
In a bowl, whisk together flour, baking powder, and salt.
In another bowl, beat butter and sugar until light and fluffy.
Add eggs one at a time, then mix in vanilla extract.
Gradually add dry ingredients and milk, alternating between the two.
Divide batter evenly into three bowls. Leave one plain, color one red, and one blue.
Pour each batter into prepared pans and bake for 20–25 minutes.
Let cakes cool completely before removing from pans.
For frosting, beat butter until creamy, then add powdered sugar, milk, and vanilla.
Layer the cakes, spreading frosting between each layer.
Frost the outside evenly and decorate as desired.