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 on the box.
Next, divide the batter into four equal portions, adding a few drops of food coloring to each bowl, and stir well. Using a spoon, drop small portions of each colored mixture into the bottom of the baking dish. The batter will spread in the greased dish, so work quickly. Start by dropping one color at a time, leaving a few inches between the drops, and then proceed with the next color, continuing until the bottom of the pan is covered. Add another layer of each color until all the batter is used. Once done, gently tap the baking dish on the counter to level the surface—avoid spreading with a spatula to keep the colors intact. With a toothpick, swirl the colors just a little; do not overmix, as you want the colors to swirl but not blend. Bake the cake as directed on the box.
Once baked, allow the cake to cool at room temperature for about 10 minutes. Then, using the handle end of a wooden spoon, poke holes all over the top of the cake, spacing them nearly an inch apart. Let the cake cool completely.
In a bowl, whisk together the white chocolate pudding mix and milk until the pudding dissolves. Before the pudding sets, pour it evenly over the cooled cake, making sure to fill the holes completely. Spread any remaining pudding on top, then refrigerate to allow it to set fully.
Once the pudding is set and the cake has cooled completely, prepare the whipped cream. Beat chilled heavy cream and vanilla extract until soft peaks form, then add powdered sugar and continue mixing until stiff peaks form. Spread the whipped cream over the pudding layer.
Garnish the cake with sprinkles before serving.
Store any leftovers in the fridge.