Start by preheating your oven to 160°C (320°F). Prepare your baking pan by greasing it and lining it with parchment paper for easy cake removal.
In a large mixing bowl, beat together the melted butter and powdered sugar until well combined.
Add the eggs one at a time, beating at high speed after each addition. Stir in the vanilla extract after incorporating the eggs.
In a separate bowl, combine the all-purpose flour, baking powder, and baking soda.
Gradually add half the flour mixture to the egg batter, mixing at low speed. Follow this with half of the milk, and continue to mix.
Add the remaining half of the flour mixture and the remaining milk, and mix until the batter is smooth.
Divide the batter in half. Add the cocoa powder to one-half and mix thoroughly to create a chocolate batter.
Create layers in your prepared baking pan by alternating between the vanilla and chocolate batters.
Use a knife or skewer to create a marbling effect by swirling the batters together.
Bake the cake in the preheated oven for 45-50 minutes or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan, then transfer it to a wire rack to cool completely.
Slice, serve, and enjoy your delectable classic marble cake!