Preheat oven to 350 degrees F (175 degrees C). Grease and flour an 8-inch square pan.
In a medium bowl, cream together the butter and sugar until light and fluffy. Beat in the eggs one at a time, then stir in the vanilla. Combine the cocoa, flour, baking powder, baking soda and salt; stir into the creamed mixture alternately with the milk.
Pour batter into prepared pan. Bake in preheated oven for 30 to 40 minutes, or until a toothpick inserted into center of cake comes out clean.