At least one hour before starting the frosting recipe, take out the stick of butter and the cream cheese to allow them plenty of time to soften to room temperature. This step is crucial to success of the frosting.
For the cake: Preheat oven to 350F degrees. Butter a 9-inch springform pan and line the bottom with parchment paper.
In a large saucepan, combine stout beer and butter. Place over medium heat until butter melts, then remove from heat. Add the 3/4 cup cocoa and 2 cups sugar, then whisk to blend.
In a small bowl, combine the 3/4 cup sour cream, 2 eggs, and 1 tablespoon vanilla; mix well. Add this to the beer/butter mixture. Add the 2 cups flour, the 2 1/2 teaspoons baking soda, then whisk again until smooth. Pour batter into the buttered pan, bake for 45 minutes to one hour, until risen and firm. Test with a tooth pick and if it comes out clean, it's ready. Place pan on a wire rack and cool completely in the pan.
For the frosting: In a stand mixer with flat paddle attachment, beat the 8 tablespoons of softened butter on medium speed until creamy. Reduce speed to low and add the 5 cups confectioners' sugar, one cup at a time. This mixture will remain powdery at this point. Now add the 8 ounces of softened cream cheese, one large scoop at a time (add in about 1/4 of the cream cheese at a time). The frosting will be creamy now. Still on low speed, add the Irish cream, one tablespoon at a time. Increase the speed to medium high and beat the frosting for about 2 to 3 minutes, until light and fluffy and increased in size.
To frost the cake, you can use an off-set spatula to smooth over the top of the cake, leaving the sides bare or you can cover the entire cake. For a unique look, you can also place the frosting in a pastry bag with a large round tip (1cm) and starting in the center, spiral the frosting out to the edge of the cake.
Serve immediately or refrigerate for at least 30 minutes to set the frosting before cutting. This will prevent the frosting from seeping over the edges as it is cut. This cake is even better the day after baking/frosting as the beer and Irish Cream mellow out just enough to really present a rich but smooth taste. Cover any leftover cake with plastic wrap and refrigerate up to a week.