Preheat the oven to 180 C / Gas 4. Grease and flour a 23cm cake tin.
Beat the butter and sugar in a mixer until light and fluffy. Add the egg yolks, flour, baking powder and vanilla extract and mix well. Divide the cake mixture into two bowls. Stir the cocoa into one of the bowls.
Beat the egg whites until stiff. Divide into 2 equal parts, and fold one part of the egg whites into each mixture.
Pour the vanilla cake mixture into the prepared cake tin. Add large spoonfuls of the chocolate mixture over the top and swirl with a spatula to create a marbled effect.
Bake in the preheated oven until a skewer inserted near the centre comes out clean, about 40 minutes. Let cool for 10 minutes in the tin, then remove to a wire rack to cool completely.