Preheat the oven to the temperature indicated on the cake mix box. Grease a 9x13-inch baking dish with baking spray and set it aside.
Prepare the cake mix according to the instructions provided on the box.
Next, divide the batter into 4 equal portions. Add a few drops of food coloring to each portion and stir well to combine.
Using a spoon, drop small spoonfuls of each colored batter onto the bottom of the prepared baking dish. The drops will spread out in the greased dish, so work quickly. I recommend dropping one color at a time, leaving a few inches between each drop. Start with one color, then add the next, followed by the third and fourth colors until the bottom of the pan is covered. Add another layer on top until all the batter is used up.
Once all the batter is in the pan, gently tap the baking dish on the counter to flatten the surface. Avoid using a spatula to spread the batter, as this could mix the colors. Using a toothpick, swirl the colors lightly to create a marbled effect—do not over-mix, as you want the colors to swirl, not blend together.
Bake the cake as directed on the box.
After baking, let the cake sit at room temperature for about 10 minutes. Then, using the handle of a wooden spoon, poke holes all over the top of the cake, spacing them about an inch apart. Allow the cake to cool completely.
In a separate bowl, whisk together the white chocolate pudding and milk until the pudding is fully dissolved. Before the pudding sets, pour it over the cooled cake, making sure to fill all the holes. Spread any remaining pudding on top of the cake and refrigerate to let it set completely.
Once the pudding has set and the cake has cooled, prepare the whipped cream topping. Whisk chilled heavy cream and vanilla extract together until soft peaks form. Gradually add the powdered sugar and continue mixing until stiff peaks form. Spread the whipped cream over the pudding layer.
Garnish with sprinkles just before serving.
Store the cake in the fridge.