Heat oven to 350°. Grease a 13 x 9-inch baking pan.
In a large bowl, beat butter and sugar until smooth, about 2 minutes. Beat in eggs and cocoa powder. On low speed, beat in flour, baking soda, water and milk until combined. Beat for 1 minute on medium-high speed.
Pour into prepared pan and bake at 350° for 40 minutes or until a toothpick inserted into the center comes out clean. Remove from oven; cool on a wire rack.
In a medium-size bowl, beat together butter and cocoa powder. Add confectioners sugar and milk alternately, beating on medium speed until it reaches a good spreading consistency. Beat in vanilla extract.
Frost top of cake and refrigerate for at least 30 minutes for frosting to firm up.
Makes 16 servings.