Beat sugar and butter until pale. Add eggs and mix well. Sift in flour, and cocoa powder. Add milk and mix well. Bake in a preheated oven at 160˚C for seven minutes. Make buttercream: Beat butter and shortening together until pale. Cook water and sugar together. Beat eggs until foamy, then, while the mixer is running, slowly drizzle in sugar syrup. Add butter mixture and beat on medium speed for fifteen minutes, then turn up to high. Beat until creamy and of piping consistency. Add a little green colouring. Fill a piping bag equipped with a star nozzle and pipe out the cream to form a Christmas tree. Decorate with coloured beads and star-shaped edible decorations.