Preheat oven to 350°F (175°C). Grease a 9x13-inch baking dish.
Prepare the chocolate cake batter according to package directions using the additional ingredients listed. Pour into the prepared baking dish and bake for 25–30 minutes or until a toothpick inserted in the center comes out clean. Let cool completely.
In a medium bowl, whisk together the instant chocolate pudding mix and cold milk until thickened, about 2 minutes. Spread evenly over the cooled cake layer.
Fold the whipped topping into the pudding mixture until smooth. Spread this mixture over the pudding layer.
Sprinkle the chocolate chips evenly over the whipped topping layer.
Drizzle chocolate syrup or fudge sauce over the top. Slice and serve immediately.