Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a 9-inch fluted tube cake pan (such as Bundt®).

Combine cake mix and pudding mix in a mixing bowl using an electric mixer. Add sour cream, vegetable oil, and water; mix well. Add eggs, 1 at a time, beating well after each addition. Stir in chocolate chips. Pour batter into the prepared pan.

Bake in the preheated oven until a toothpick inserted into the center comes out clean, 55 to 60 minutes. Let cool for 10 minutes. Transfer to a cake plate and let cool completely, 20 to 30 minutes more.

Place opened frosting container in a microwave on medium heat, stirring every 30 seconds until just soft enough to pour. Drizzle frosting over cake and sprinkle candy-coated milk chocolate pieces on top.