Preheat the oven to 350 degrees F (175 degrees C). Grease a 9x13-inch baking pan.

Mix cake mix, butter, 2 eggs, and vanilla extract in a bowl. Pat into the prepared pan.

Mix cream cheese, cocoa powder, and remaining eggs together in another bowl with an electric mixer. Beat in powdered sugar slowly. Pour over cake layer in the pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, about 45 minutes. Let cool.