Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
In a large bowl, combine cake mix, eggs, oil, vanilla extract, and crushed pineapple with juice. Mix until smooth.
Pour batter into the prepared dish and bake for 30–35 minutes, or until a toothpick inserted in the center comes out clean.
Let cake cool completely before frosting.
For the frosting, mix whipped topping, drained pineapple, and pudding mix until creamy.
Spread frosting over cooled cake and refrigerate for at least 30 minutes before serving.