Preheat oven to 350°. Grease and flour 13 X 9-inch pan.
Mix cake as directed on package. Pour into pan.
Combine ricotta, sugar, eggs and vanilla; mix well. Spoon over unbaked cake. Bake for 1 hour; let cool.
Mix pudding with milk, fold in cool whip; spread over cake.
Cover with plastic wrap or foil, and store in refrigerator.