Preheat oven to 350 degrees F (175 degrees C). Grease and flour a Bundt or tube pan.
Combine cake mix, pudding mix, eggs, coffee, 3/4 cup liqueur, and oil with an electric mixer at low speed until moistened. Beat for two minutes at high speed. Pour batter into prepared pan.
Bake for 45 to 55 minutes, or until done. Cool for 30 minutes. Invert onto serving plate, and prick top with a fork.
Heat frosting in a small pan. Remove from heat, and stir in 3/4 cup liqueur. Drizzle glaze over top of cake, allowing it to soak in and drizzle over sides. Repeat until glaze is used up.