PREHEAT oven to 350° F. Lightly grease 13x9-inch baking pan; dust with cocoa.
COMBINE flour, granulated sugar and 1/3 cup cocoa in large mixer bowl. Stir in mayonnaise and vanilla extract; beat for 2 minutes. Combine warm water and baking soda in small bowl; stir until dissolved. Add to flour mixture slowly; stir until well blended. Spread into prepared pan.
BAKE for 25 minutes or until wooden pick inserted in center comes out clean. Cool completely in pan on wire rack.
WHISK together powdered sugar, remaining 2/3 cup cocoa and margarine. Add up to 3 tablespoons coffee until frosting is smooth and thick. Frost cake.