Preheat the oven to the temperature specified on the cake mix box and grease a 9x13 inch baking dish with baking spray.
Prepare the cake mix according to the package directions.
Divide the batter evenly into four bowls and add a few drops of different food coloring to each; stir well to combine.
Using a spoon, quickly drop small dollops of each colored batter onto the bottom of the greased baking dish, leaving space between drops. Repeat, layering the colors until all batter is used.
Tap the baking dish gently on the counter to flatten the surface. Swirl the colors slightly with a toothpick without overmixing.
Bake the cake as directed on the box. Allow to cool at room temperature for about 10 minutes.
Use the handle end of a wooden spoon to poke holes about an inch apart over the entire surface of the warm cake. Cool completely.
Whisk together the white chocolate pudding mix and milk until smooth. Pour the pudding over the cooled cake, filling all holes, and spread the remaining pudding on top.
Refrigerate the cake until the pudding is fully set.
Whip the chilled heavy cream with vanilla extract until soft peaks form. Add powdered sugar and continue whipping until stiff peaks form.
Spread the whipped cream over the pudding layer and garnish with sprinkles before serving.
Store the cake in the refrigerator.