Preheat your oven according to the cake mix package instructions, usually 350°F (175°C). Grease a 9-by-13-inch baking pan with cooking spray or butter to prevent the cake from sticking.
Prepare the yellow cake mix according to the package directions. Combine the cake mix with the required eggs, water, and oil, then beat until the batter is smooth. Avoid overmixing, as this can make the cake dense.
Pour the batter into the prepared baking pan and spread it evenly. Bake according to the package directions, generally 25–35 minutes, or until a toothpick inserted into the center comes out clean.
Remove the cake from the oven and allow it to cool for approximately 10–15 minutes. Use the handle of a wooden spoon or a thick straw to poke holes across the surface, spacing them about 1 inch apart. Make the holes deep enough for the pudding to reach the interior without breaking through the bottom.
In a medium bowl, whisk the instant vanilla pudding mix with 3 cups of cold milk. Whisk for approximately 1–2 minutes until the mixture begins to thicken but remains pourable. Work promptly because instant pudding sets quickly.
Pour the pudding evenly over the cake, paying particular attention to the holes. Use a spatula to gently spread the remaining pudding across the surface so that it fills the openings. Tap the pan lightly on the counter to help the pudding settle.
Place the cake in the refrigerator and chill for at least 2 hours, preferably 3–4 hours. This allows the pudding to set and the cake to absorb its creamy filling.
Once the cake is thoroughly chilled, spread the thawed whipped topping evenly over the surface. Create soft swirls with a spatula for an attractive finish.
Sprinkle chocolate shavings, colorful sprinkles, crushed cookies, or fresh berries over the topping. Choose decorations that complement your pudding flavor.
Cut the cake into 12 portions and serve chilled. Store any leftovers promptly in a covered container in the refrigerator.