Place a rack in the center of the oven. Preheat oven to 350°F. Grease and flour a 10-12-inch bundt pan (or spray with nonstick baking spray).
Add cake mix, pudding mix, sour cream, eggs, water, and oil to a large bowl. Mix with a hand mixer until smooth. Fold in sprinkles.
Pour batter into prepared pan. Bake until a toothpick comes out clean, approximately 40-45 minutes.
Cool 10 minutes in pan, then invert over serving plate to release the cake from the pan.
Allow to cool completely before frosting.
Make the frosting by mixing the butter and cream cheese with a hand mixer or stand mixer fitted with the paddle attachment. Add powdered sugar, salt, and vanilla and mix until smooth.
Add to a piping bag fit with a large round tip and pipe onto cake. If frosting seems too thin to hold it’s shape, chill 30 minutes before piping.
Add additional sprinkles and chill to set icing.
Store loosely covered in the refrigerator for up to 3 days. Cake can be made ahead and frozen with or without frosting.