Preheat oven to 350 degrees Fahrenheit (175 degrees C). Grease large Bundt pan (10-12 cups or 9-10 inches in diameter) with shortening, then dust with flour. Or you can use Baker's Joy baking spray.
In the bowl of the stand mixer, add the cake mixes, eggs, water and oil. Mix well (with the whisk attachment), scraping the sides of the bowl as needed. Mix for about 2-3 minutes. Divide the cake batter evenly between 4 or 5 bowls (depending on how many colors you have). Add food colouring to all but one bowl, leaving that bowl as white batter.
Pour batter into prepared pan, one color at a time. You may not use all the batter, depending on the size of your pan. Fill the pan only about 2/3 full so that it doesn't overflow. If you have any leftover batter, bake cupcakes.
Bake the cake for 50-60 minutes, until toothpick inserted in the center comes out clean. Cool 10 minutes before loosening the edges of the cake and turning it out onto a wire rack to cool completely.
Make glaze by adding powdered sugar, vanilla, and 2 tablespoons of milk to bowl. Mix with a whisk slowly, adding more milk one tablespoon at a time, until desired consistency is reached.
Place the cake on a cake plate. Pour the glaze slowly over the cooled cake. Add sprinkles before the glaze sets.
Store the cake in an airtight container at room temperature.
The calories shown are based on the cake being cut into 12 pieces, with 1 serving being 1 slice of glazed cake. Since different brands of ingredients have different nutritional information, the calories shown are just an estimate. **We are not dietitians and recommend you seek a nutritionist for exact nutritional information. The information in the nutrition box are calculated through a program and there is room for error. If you need an accurate count, I recommend running the ingredients through your favorite nutrition calculator.**