Preheat oven to 350°F (175°C). Grease and flour six 8-inch round cake pans.
In a medium bowl, whisk together flour, baking powder, and salt.
In a large bowl, beat butter and sugar until light and fluffy. Add eggs one at a time, beating well after each addition. Stir in vanilla.
Gradually add flour mixture, alternating with milk, beginning and ending with flour mixture. Mix until just combined.
Divide batter evenly into six bowls. Add a different food coloring to each bowl and mix well.
Pour each colored batter into prepared pans. Bake for 20-25 minutes or until a toothpick inserted into the center comes out clean.
Cool in pans for 10 minutes, then transfer to wire racks to cool completely.
Frost and stack the cake layers as desired.