Preheat the oven to 350 degrees F. Spray a 6 by 3-inch high cake pan with nonstick cooking spray and set aside.
In a large mixing bowl, combine the cake mix, eggs, butter, and milk. Using a hand mixer, beat on medium speed for 2 minutes, scraping down the sides of the bowl to be sure the batter is well incorporated. Fold the dulce de leche into the batter, but do not completely incorporate. Fill the cake pan 2/3 of the way to the top. Make cupcakes with the remaining batter. Line a muffin tin with paper liners and using an ice-cream scoop, fill the muffin tins with batter. Bake the cupcakes for 10 to 12 minutes, and the cake for 20 to 25 minutes. The tops should be golden brown, and a toothpick inserted into the center of the cake comes out clean. Remove from the oven and cool 10 minutes before unmolding and cooling completely on a wire rack, right side up.
Frosting: In a mixing bowl, beat together the vanilla frosting and the dulce de leche until well incorporated. Add enough confectioners' sugar to make the frosting thick but spreadable.
To decorate the cake, use a serrated knife to cut the top of the cake to make it flat. Adhere the cake to a 6-inch cardboard cake board, and ice the top and sides of the cake with frosting in a swirl pattern. Decorate the top with gold dragees, and the number candles. Frost the cupcakes and arrange them on a serving platter.