1. Prepare Coffee Mixture: In a bowl, combine the chilled coffee and dark rum.

2. Beat Egg Whites: Using an electric mixer, beat the egg whites until they form stiff peaks. Set aside.

3. Mix Egg Yolks and Mascarpone: In a separate bowl, mix the egg yolks with the sugar and mascarpone cheese until the mixture is smooth and homogeneous. Gently fold in the beaten egg whites.

4. Prepare the Pan: Using a small sieve, sprinkle cocoa powder evenly over the bottom of a 9-inch springform pan.

5. Layer the Ladyfingers: Quickly dip each ladyfinger into the coffee mixture and arrange them to cover the bottom of the pan.

6. Layer the Filling: Spread one-third of the mascarpone mixture over the ladyfingers. Sprinkle with cocoa powder. Repeat the layering process two more times, ending with a layer of cocoa powder on top.

7. Chill and Serve: Refrigerate the cake until it is well chilled. Serve and enjoy!