To prepare the cake layers – Preheat oven to 350 degrees. Spray three 8-inch cake pans with nonstick food spray. Line the bottoms of the pans with parchment paper and spray with nonstick food spray.
Combine the beer and 2 cups of butter in a saucepot. Place over medium heat. When melted, whisk in the cocoa powder. Whisk until smooth. Transfer the mixture to a mixing bowl. Set the bowl over another bowl filled with ice. Whisk the chocolate mixture over the ice until cooled, about 5 minutes.
Place the eggs and sour cream in the bowl of a mixer fitted with a flat beater. Beat until combined. Add the beer mixture and beat on low speed until just combined. Add the flour mixture in 3 additions, beating briefly after each addition. Divide the cake batter evenly between the prepared cake pans. Bake cakes for 35 to 40 minutes, or until a toothpick inserted into the center of the cakes comes out clean. Cool the cakes in the pans for 15 minutes. Carefully turn the cakes out onto a cooling rack and let cool completely.
To make the frosting – Cream the room temperature butter and cream cheese in the bowl of a mixer until smooth. Add the vanilla extract and mix to combine. Lower the speed to medium- low and gradually add the powdered sugar. When all the sugar is added, increase the speed to medium high and beat for one minute.
To finish the cake – Use a serrated knife to even out the top of the cakes. Frost the top of two cake layers with 2/3 of the frosting. Place cakes on top of each other. Frost the top cake layer with the remaining frosting. Refrigerate until ready to serve. Let sit at room temperature for 20 minutes before serving.