Preheat the oven to 325 degrees F (165 degrees C). Grease a 3-quart casserole dish.
Beat butter and sugar together using a hand mixer until creamy. Add eggs one at a time, beating well after each addition. Mix in sour cream. Alternate adding in corn bread mix and milk; beat well after each addition. Fold in corn kernels and cream-style corn. Pour mixture into the prepared dish.
Bake in the preheated oven until pudding is set and light brown in color, 45 to 50 minutes.