Grease a 9 x 13-inch baking pan and preheat the oven to 350°F. Prepare the white cake mix with the 3 eggs, 1 cup water, and 1/2 cup vegetable oil, following the package directions, then spread the batter evenly in the prepared pan.

Bake the cake at 350°F for 25 to 30 minutes, or until the center springs back lightly and a toothpick inserted in the middle comes out clean. Set the pan on a cooling rack and let the cake cool for about 15 to 20 minutes.

Prepare the red gelatin in a small bowl with 1/2 cup boiling water and 1/4 cup cold water. Stir until the gelatin is completely dissolved, then prepare the green gelatin separately with the remaining 1/2 cup boiling water and 1/4 cup cold water.

Use the handle of a wooden spoon or a large straw to make holes throughout the cake, spacing them about 1 inch apart. Do not push the tool all the way to the bottom, because the gelatin should remain distributed inside the cake rather than collect underneath it.

Pour the red and green gelatin into alternating holes, working slowly so each color sinks into the cake. If gelatin begins to pool on the surface, pause briefly and allow it to absorb before adding more.

Cover the pan and refrigerate the filled cake for at least 1 hour, preferably 2 hours, until thoroughly chilled and set. The cake can also be refrigerated overnight for especially clean slices.

Spread the thawed whipped topping over the completely chilled cake in an even layer. Scatter 2 to 3 tablespoons of Christmas sprinkles over the top just before serving, and keep the finished cake refrigerated.