Preheat the oven to 180°C (approximately 350°F). Grease a bundt cake pan with butter and sprinkle with breadcrumbs.
Melt the butter and let cool briefly. Mix the buttermilk, applesauce, sugar, egg, vanilla sugar and rum extract until creamy. Gradually stir in the butter.
Mix the flour, baking powder and baking soda. Fold the flour mixture into the butter mixture.
Pour about half of the batter into the pan. Stir the cocoa powder into the remaining batter. Pour the darker batter onto the lighter batter and gently stir with a fork, creating a marbled pattern.
Bake for about 50 minutes. Remove from the oven and let cool on a wire rack. Serve dusted with powdered sugar.