Preheat oven to 350°F/180°C. Butter three 9-inch cake pans, and line the bottoms with parchment paper.
Cake: In a medium bowl, sift together flour, baking powder, and salt. Set aside.
In the bowl of an electric mixer fitted with the paddle attachment, beat butter, oil, and sugar on medium speed until light and fluffy, 3-4 minutes. Scrape down the sides and bottom of the bowl as needed. Add eggs, one at a time, beating well after each addition. Beat in vanilla extract. With the mixer on low speed, add the flour mixture in three additions alternating with the milk in two additions, beginning and ending with the flour mixture. Do not overmix the batter. The less you mix, the lighter the cake will be. Divide the batter as evenly as possible into three bowls. Add food coloring to each bowl until desired color is reached. Add just a tiny drop at first because food colorings can be very concentrated.
Pour each bowl of batter into prepared pans. Bake for 25-30 minutes until a toothpick inserted into the center of the cakes comes out clean. Allow cakes to cool for 15 minutes, then gently remove from pans and allow them to cool completely on a wire rack.