Preheat oven to 350 degrees F (175 degrees C). Line a 10x16-inch baking pan with aluminum foil.
Combine 1 cup white sugar, eggs, oil, and vanilla sugar in the bowl of a stand mixer fitted with the paddle attachment. Beat until smooth and creamy.
Combine remaining 2 cups white sugar, boiling water, and cocoa powder in a separate bowl; stir until sugar is dissolved.
Stir cocoa mixture into beaten eggs. Add flour, baking powder, and rum extract gradually, beating until fully blended. Pour batter into the prepared pan.
Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 1 hour 10 minutes.
