Preheat oven to 325 degrees F.
Grease bundt pan with either non-stick cooking spray or shortening.
With an electric mixer, mix together eggs, cake mix, pudding mix, oil, water and sour cream.
Separate batter equally into three separate bowls. Add 3-4 drops green food coloring to one bowl and 3-4 drops red food coloring to another bowl. Stir each bowl to make red batter and green batter.
Grease a bundt cake pan with non-stick cooking spray or coat with shortening. Start by adding green batter to pan then layer with red batter and then white batter.
Bake for approximately 50 minutes or until toothpick inserted comes out clean.
Once baked, remove from the oven and let cool for about 10 minutes. Turn the cake out on a cake plate and let cool.
In a bowl, stir together milk and powdered sugar to make icing. Drizzle on top of cake and the add sprinkles.