Buttercream Frosting: In a large bowl with a mixer on low speed combine powdered sugar, cocoa, butter, milk, and vanilla. Beat at medium speed 1-2 minutes until creamy.
For Fudge Frosting: Combine all ingredients in a saucepan. Bring to a rolling boil. Stir constantly and cook for 2 minutes. Remove from heat. Beat until mixture just starts to thicken.