Bake the Cake:
Preheat oven to the temperature indicated on the cake mix box.
Prepare the cake batter according to the instructions on the box, using the ingredients listed on the box (usually eggs, oil, and water).
Pour the batter into a greased and floured 9×13 inch baking pan.
Bake according to the box instructions, or until a toothpick inserted into the center comes out clean.
Let the cake cool completely in the pan.
Prepare the Pudding Filling:
In a large mixing bowl, whisk together the instant vanilla pudding mix and the milk until smooth.
Let the pudding mixture sit for 5 minutes to thicken slightly.
Poke and Fill the Cake:
Once the cake has cooled completely, use the handle of a wooden spoon or spatula to poke holes all over the cake, about 1 inch apart. Make sure the holes go almost all the way to the bottom of the cake, but not through it.
Slowly pour the pudding mixture evenly over the cake, allowing it to seep into the holes.
Cover the cake and refrigerate for at least 2 hours, or preferably longer, to allow the pudding to set completely and the cake to become moist.
Frost and Serve: