Allow butter and eggs to stand at room temperature for 30 minutes. Meanwhile, lightly grease bottoms of two 8x8x2-inch square or 9x1-1/2-inch round cake pans. Line bottom of pans with parchment or waxed paper. Grease and lightly flour bottoms and sides of pans. Or, grease one 13x9x2-inch baking pan. Set pan(s) aside.
In a mixing bowl stir together flour, cocoa powder, baking soda, baking powder; and salt; set aside.
In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Gradually add sugar, about 1/4 cup at a time, beating on medium speed until well combined (3 to 4 minutes). Scrape sides of bowl; continue beating on medium speed for 2 minutes. Add eggs, one at a time, beating after each addition (about 1 minute total). Beat in vanilla.
Add flour mixture and milk alternately to beaten mixture, beating on low speed just until combined after each addition. Beat on medium to high speed for 20 seconds more. Spread batter evenly into the prepared pans.
Bake in a 350 degree F oven for 35 to 40 minutes for 8-inch pans and 13x9x2-inch pan, 30 to 35 minutes for 9-inch pans, or until a wooden toothpick inserted in the center comes out clean. Cool cake layers in pan for 10 minutes. Remove from pans. Peel off paper. Cool thoroughly on wire rack. Or, place 13x9x2-inch cake in pan on a wire rack; cool thoroughly. Frost with desired frosting. Makes 12 to 16 servings.