Preheat the oven to the temperature specified on the cake mix box. Grease a 9×13-inch baking dish with baking spray and set it aside. Prepare the cake batter according to the instructions on the box. Divide the batter evenly into four bowls and add a few drops of different food coloring to each, stirring well to combine. Using a spoon, drop small dollops of each colored batter onto the bottom of the prepared baking dish. Work quickly, as the batter will spread in the greased pan. Start by dropping one color at a time, spacing the dollops a few inches apart, then repeat with the second, third, and fourth colors until the bottom is covered. Continue layering dollops on top until all the batter is used. Gently tap the baking dish on the countertop to level the surface, avoiding using a spatula to prevent the colors from blending together. Use a toothpick to lightly swirl the colors for a marbled effect—be careful not to overmix, as you want distinct swirls, not fully blended colors. Bake the cake according to the time stated on the box.

Once baked, let the cake sit at room temperature for about 10 minutes. Using the handle of a wooden spoon, poke holes evenly across the top of the cake, about an inch apart. Allow the cake to cool completely. In a bowl, whisk together the white chocolate pudding mix and milk until smooth and fully dissolved. While the pudding is still pourable but beginning to thicken, pour it evenly over the cooled cake, making sure to fill all the holes. Spread any remaining pudding over the surface. Refrigerate the cake until the pudding sets completely.

When the pudding layer is set and the cake is fully chilled, prepare the whipped cream topping. Beat the chilled heavy cream and vanilla extract until soft peaks form. Add powdered sugar and continue beating until stiff peaks form. Spread the whipped cream evenly over the pudding layer. Decorate with sprinkles before serving. Store the cake in the refrigerator.