Preheat the oven to 350°F (175°C) and grease the bundt pan.

In a mixing bowl, cream together the butter and sugar until light and fluffy.

Add the eggs one at a time, mixing well after each addition.

Stir in the milk and vanilla extract.

In another bowl, whisk together the flour, baking powder, and salt.

Gradually add the dry ingredients to the wet ingredients, mixing until just combined.

Divide the batter into separate bowls and add food coloring to each bowl.

Spoon the colored batters into the prepared bundt pan, swirling them together.

Bake for 45-50 minutes or until a toothpick inserted comes out clean.

Let the cake cool in the pan for 10 minutes before inverting onto a wire rack.