Heat oven to 350°F. Grease and flour two 9-inch round pans or one 13x9x2-inch baking pan.
Stir together sugar, flour, cocoa, baking powder, baking soda and salt in large bowl. Add eggs, milk, oil and vanilla; beat on medium speed of electric mixer 2 minutes. Stir in boiling water (batter will be thin). Pour batter into prepared pans.
Bake 30 to 35 minutes for round pans, 35 to 40 minutes for rectangular pan or until wooden pick inserted in center comes out clean. Cool 10 minutes; remove from pans to wire racks. Cool completely. (Cake may be left in rectangular pan, if desired.)
For icing: Beat butter in medium bowl. Add powdered sugar and cocoa alternately with milk, beating to spreading consistency (additional milk may be needed). Stir in vanilla. About 2 cups frosting.