Preheat the oven to 350°F/180°C. Grease 3 x 9-inch pans with shortening or butter and dust with a tablespoon of flour each. Set pans aside.
In a large bowl, cream together the butter and sugar with an electric mixer on medium speed. Add the eggs, one at a time, and make sure each egg is fully incorporated before adding the next. Add the vanilla extract, and beat until well blended.
In a separate medium bowl, sift and then whisk together the flour, baking powder, baking soda, and salt to make sure it’s thoroughly combined. With a wooden spoon or spatula, gradually fold in the dry ingredients to the wet ingredients, alternating adding the flour and the buttermilk, until just barely combined. Do not over-mix the batter.
Divide the batter equally into three small or medium bowls. (It’s best to use a digital kitchen scale to make sure the weights are equal.) Add a drop of the pink, blue, and yellow food coloring separately to each bowl of batter. Stir the batter gently until the color is well mixed. Pour each batter into each of the 3 cake tins.
Bake on the middle rack of the oven for 20-25 minutes, or until a toothpick inserted in the middle comes out clean. Let the cakes cool in the tin for about ten minutes, then transfer them to a cooling rack to cool the cakes completely.