Begin by gathering all necessary ingredients. Preheat your oven to 350 degrees Fahrenheit (175 degrees Celsius) and proceed to grease and flour three 9-inch round cake pans.

To prepare the cake, combine the cake mix, water, egg whites, and vegetable oil in a large mixing bowl. Using an electric mixer set to medium speed, blend until the mixture is thoroughly combined, which should take approximately 2 minutes. Distribute two-thirds of the batter evenly between two of the prepared pans. Stir the instant coffee into the remaining batter before pouring it into the third prepared pan.

Bake the cakes in the preheated oven for 23 to 28 minutes, or until a toothpick inserted into the center of each cake comes out clean. Allow the cakes to cool in the pans for 10 minutes before inverting them onto a wire rack to cool completely.

While the cakes cool, prepare the coffee syrup by mixing the brewed coffee with the coffee liqueur in a measuring cup; set aside for later use.

For the filling, beat the mascarpone cheese, confectioners' sugar, and coffee liqueur together in a medium bowl with an electric mixer on low speed until the mixture is smooth. Cover with plastic wrap and refrigerate to maintain its cool temperature.

To make the frosting, whip the heavy cream, confectioners' sugar, and coffee liqueur in a medium bowl with an electric mixer set to medium-high speed until stiff peaks form. Gently fold half a cup of this whipped frosting into the chilled filling until fully combined. Store both the frosting and filling in the refrigerator, covered, until ready to use.

To assemble the cake, place one plain cake layer on a serving platter. Using a thin skewer, poke holes into the cake about one inch apart. Pour one-third of the coffee syrup over the layer, then spread half of the filling on top. Position the coffee-flavored cake layer next, poking holes into this layer as well. Drizzle another third of the coffee syrup over this layer and top it with the remaining filling. Finally, add the last cake layer, poke holes in it, and pour the remaining coffee syrup over the top. Spread the frosting evenly across the top and sides of the cake.

For the finishing touch, sift cocoa powder through a sieve to lightly dust the top of the cake. Use a vegetable peeler to create chocolate curls from the semisweet chocolate square and scatter these curls over the cake.

Refrigerate the assembled cake for a minimum of 30 minutes before serving to allow the flavors to meld and the texture to set.