Preheat oven to 350°F. Grease a 9x13-inch baking dish and set aside.

Prepare the white cake mix according to the package directions, adding the 2 teaspoons vanilla extract to the batter.

Divide the batter evenly into 3 bowls. Stir blue gel food coloring into one bowl, purple gel into a second bowl, and pink gel into the third bowl.

Alternating colors, drop heaping spoonfuls of the three batters randomly into the prepared baking dish until all batter is used.

Bake 25–30 minutes or until a toothpick inserted in the center comes out clean. Cool in the pan for 10 minutes.

Using the end of a wooden spoon (or similar tool), poke large holes all over the warm cake.

In a medium microwave-safe bowl combine the 2 cups condensed milk and 2 cups white chocolate chips. Microwave 1 minute, stir until combined and the chocolate is melted; if needed microwave an additional 30 seconds and stir until smooth.

Pour the condensed milk/white chocolate mixture evenly over the cake, allowing it to seep into the holes.

Prepare each 3.4-ounce pudding mix according to its package directions, using a total of 4 cups milk (2 cups milk per pudding mix). Stir each pudding until it begins to thicken.

Immediately pour the prepared vanilla pudding over the cake first, pressing it into the holes, then add the prepared strawberry pudding and spread evenly over the cake.

Let the cake come to room temperature, then refrigerate for at least 6 hours to set.

After chilling, frost the cake with the 8-ounce container of whipped topping and sprinkle the 1/3 cup sprinkles over the top.

Refrigerate at least 1 hour more before serving.