Preheat an oven to 350 degrees F (175 degrees C). Line two 12 cup muffin pans with paper baking cups. Stir together the flour, baking powder, baking soda, and salt in a large bowl. Whisk together the milk, vegetable oil, and vanilla extract in a separate bowl until evenly blended; set aside.
Beat the butter and sugar with an electric mixer in a large bowl until light and fluffy. The mixture should be noticeably lighter in color. Add the room-temperature eggs one at a time, allowing each egg to blend into the butter mixture before adding the next. Pour in the flour mixture alternately with the milk mixture, mixing until just incorporated.
Divide the cake batter into four separate bowls. Add a few drops of food coloring into one bowl of batter and stir; add more food coloring, if necessary, to reach the desired shade. Repeat with the remaining colors and bowls of batter.
Using a different spoon for each color batter, spoon a small spoonful of each color into the cupcake liners, until 1/2 to 3/4 full. Do not mix the batter once it is in the cupcake liner. Bake in the preheated oven until a toothpick inserted into the cake comes clean, about 15 to 20 minutes.