Preheat oven to 350°F. Grease and flour a 10-cup Bundt pan. I use nonstick cooking spray and then thoroughly flour all the little nooks and crannies.
In a large mixing bowl, combine the cake mix, pudding mix, sour cream, eggs, oil, milk, and vanilla extract. Beat until combined.
Add the eggs one at a time. Beat at medium speed for about 2 minutes until smooth.
Gently fold in the rainbow sprinkles with a spatula, being careful not to overmix (this helps prevent color bleeding).
Spoon the batter into the prepared bundt pan and spread it evenly. Bake for 55-60 minutes, or until a toothpick inserted in the center comes out clean.
Let the cake cool in the pan for 10 minutes, then carefully turn it out onto a wire rack to cool completely.
Make the Frosting: In a mixing bowl, beat the cream cheese and butter until smooth and creamy. Gradually add powdered sugar and vanilla extract, beating until fluffy. If the frosting is too thick, add heavy cream, 1 teaspoon at a time, until it reaches a thick but pipeable consistency.
Transfer the frosting to a piping bag with a large round tip (or use a zip-top bag with the corner snipped). Pipe thick ribbons of frosting from the top of the cake down the sides to mimic the signature nothing bundt cake look.
Slice and enjoy your soft, moist confetti cake—just like the famous bakery version!