Prepare cake mix as instructed on box. Divide batter into two bowls and add red food coloring to one half and green food coloring into the other half. Pour into 9" round cake pans and bake according to instructions on box.
Melt chocolate squares over low heat and add sugar and water. Heat until smooth. Add beaten egg yolks slowly to mixture stirring quickly. Heat until thick. Let cool for a bit. Beat egg whites until stiff and fold into chocolate mixture.
Line a large mixing bowl with plastic wrap. Cut each half of the cake into squares. Checker a layer of green and red cake squares in the bottom of bowl and cover that layer with some of the chocolate mixture. Repeat until cake squares are all that is left on top of bowl. Pour any remaining chocolate mixture over the finished product.
REFRIGERATE. Turn bowl upside down on a plate and remove plastic wrap. Ice with Cool Whip or whipped cream. Serve.