Preheat oven to 350°F (175°C). Grease and line six 8-inch round pans or bake in batches using two 8-inch pans.
Whisk flour, sugar, baking powder, and salt in a bowl. Beat butter until creamy, add eggs one at a time, then vanilla.
Alternate adding dry mix and milk, starting and ending with dry mix. Divide batter into six equal bowls.
Tint each bowl a different color with gel food coloring. Pour into pans and bake 12–14 minutes, or until a toothpick comes out clean.
Cool layers 15 minutes in pans, then on a rack. Trim domes if needed for flat stacking.
Stack layers with a thin coat of white buttercream between each. Crumb-coat, chill 15 minutes, then finish with a smooth white layer.