Preheat your oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a medium bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large mixing bowl, cream together the softened butter and sugar until light and fluffy.
Add the eggs one at a time, beating well after each addition. Stir in the vanilla extract.
Gradually add the dry ingredients to the wet ingredients, alternating with the milk. Begin and end with the dry ingredients, mixing just until combined.
In a separate bowl, take about 1 to 1.5 cups of the batter. Mix in the cocoa powder, creating the chocolate batter.
Drop alternating spoonfuls of the vanilla and chocolate batters into the prepared cake pan. Use a knife or skewer to gently swirl the batters together for the marble effect.
Bake in the preheated oven for 30-35 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for about 10 minutes, then transfer it to a wire rack to cool completely.
Once cooled, slice and enjoy your homemade marble cake!