Beat the butter with the sugar. Add the 4 yolks 1 by 1 to the sifted flour with the baking powder and yoghurt. Beat the egg whites with vanilla into snow and while gently stirring, add them to the mixture.
In a greased and floured cake form, put 2/3 of the mixture and mix the rest with the cocoa and rum and pour it on top. Bake in a moderate 356°F (180 °C) oven with the fan on for 10 min on the lower element and 20-25 min with both elements on.
Check for readiness with a stick.