Combine flour and sugar in mixing bowl. In a saucepan put butter, shortening, cocoa, and water and bring to a boil. Pour into flour and sugar mixture and beat well. Add other ingredients and mix well. Bake at 400 degrees for 30 minutes.
Bring to a boil the butter, cocoa, and milk, stirring constantly to keep from burning. Remove from heat and add other ingredients. Make icing five minutes before cake has finished baking and spread on hot cake.