Preheat oven to 350 degrees F. Grease a 13x9 inch pan or glass baking dish.
Mix cake ingredients together. Beat for about two minutes on medium speed or until smooth. Pour into pan and bake at 350 degrees for about 25 to 30 minutes or until a chopstick or skewer inserted in middle comes out clean.
Let the cake cool for about 30 minutes.
Whisk together the pudding and milk. Mixture will thicken as you whisk. Use a chopstick, a metal skewer or a straw to poke holes in cake, then pour pudding mix over cake so that it falls down into the holes. You'll end up with pudding in the holes and all over the top of the cake. Spread it evenly and keep cold while you whip the cream.
Beat cream and sugar until soft peaks form, then add vanilla and continue to beat until peaks are stiff. Spread sweetened whipped cream over the pudding.