Separate egg yolks and whites. Beat the butter until frothy. Gradually add the sugar, vanilla sugar (and possibly the rum) and the egg yolks alternately. Mix everything together in approx. 10 minutes to a smooth dough. Alternately stir in the sifted flour mixed with the baking powder with the milk and then loosely fold in the egg white, which has been beaten until stiff in the meantime. Take out 1/3 of the dough and mix with the cocoa, mixed with milk and sugar.
Alternately fill both doughs into a greased tin and bake at 180 degrees for about 1 hour. Sprinkle the cooled cake with powdered sugar.