Prepare the white cake according to the box directions. Allow the cake to cool completely.
Using a bamboo skewer, poke holes in the cake with about 1 inch between holes.
Add the orange gelatin mix into a small mixing bowl or a 2-cup measuring cup.
Stir in the boiling water. Continue stirring until the gelatin is completely dissolved.
Stir in the cold water. Continue stirring for 30 seconds to 1 minute.
Spoon, or pour, the gelatin into the holes in the cake.
Cover and chill in the refrigerator for 2 hours.
After the cake has chilled, add the instant vanilla pudding mix to a medium-sized mixing bowl.
Whisk in the milk. Continue whisking for about 1 minute until the pudding begins to thicken.
Fold in the whipped topping.
Evenly sprinkle the chopped mandarin oranges over the top of the cake.
Using a silicone spatula or an offset spatula, evenly spread the pudding mixture over the chopped mandarin oranges. Cover and chill in the refrigerator for 2 more hours.
Just before serving, add the 1½ cups of whipped topping to a disposable piping bag or a quart-size Ziploc with a corner snipped off.
Slice the 15 slices measuring 2½ inches by 3 inches each.
Gently squeeze out 15 silver dollar-sized dollops (about 1½ tablespoons each). Place 1 of the mandarin orange sections on each of the whipped topping dollops. Keep the cake refrigerated until ready to serve.