Step 1
Preheat oven to 350 degrees F (175 degrees C).
Step 2
Grease a 10-inch fluted tube pan (such as a Bundt®) and coat inside of pan with unsweetened cocoa powder.
Step 3
Beat cream cheese confectioners' sugar 1 egg and Irish cream liqueur in a bowl until smooth and creamy. Set aside.
Step 4
Beat chocolate cake mix chocolate pudding mix 3 eggs and vegetable oil in a separate bowl until batter is thick and smooth. Slowly beat Irish stout beer into the batter.
Step 5
Spoon 1/3 of the cake batter into the prepared pan; layer the Irish cream filling on top. Spoon remaining cake batter over the filling.
Step 6
Bake in the preheated oven until a toothpick inserted into the cake comes out clean 40 to 50 minutes.
Step 7
Loosen the edges of the cake from the pan with a thin spatula; let cake rest in pan 15 minutes. Invert pan over a wire rack to release cake and allow to cool completely on the rack.
Step 8
While cake is cooling melt butter in a saucepan over medium heat and stir in white sugar and Irish whiskey. Bring to a boil stirring to dissolve sugar reduce heat to low and simmer until thickened about 10 minutes.
Step 9
Transfer cake to a serving platter. Generously brush whiskey glaze over cooled cake several times and allow glaze to soak into cake.