Preheat oven to 350°F (180°C). Grease and flour two 9-inch (1.5 L) round baking pans or one 9 x 13-inch (3.5 L) baking pan.
Stir sugar with flour, cocoa, baking powder, baking soda and salt in a large bowl. Add eggs, milk, oil and vanilla. Beat with an electric mixer, on medium speed, for 2 minutes. Stir in boiling water (batter will be thin). Divide batter evenly between prepared pans.
Bake for 30 to 35 minutes for the round pans (35 to 40 minutes for the large pan) or until a wooden pick inserted in the centre comes out clean. Cool for 10 minutes on a rack. Turn cakes out from pans; cool completely. (Sheet cake may be left in pan if desired.)