Preheat oven to 350 degrees F (175 degrees C). Grease and flour 3 (9 inch) pans.

Prepare the cake mix according to package directions. Divide two thirds of batter between 2 pans. Stir instant coffee into remaining batter; pour into remaining pan.

Bake in the preheated oven for 20 to 25 minutes, or until a toothpick inserted into the center of the cake comes out clean. Let cool in pan for 10 minutes, then turn out onto a wire rack and cool completely. In a measuring cup, combine brewed coffee and 1 tablespoon coffee liqueur; set aside.