Preheat the oven to 350°F. Grease a 10-inch bundt pan well.

Combine cake mix, pudding, vanilla, sour cream, eggs, vegetable oil, and 4.5 tbsp rum in a mixing bowl.

Beat with an electric mixer for 5 minutes. The batter will be stiff.

Fold in chocolate chips with a spoon or spatula.

Pour batter into the prepared bundt pan.

Bake for 1 hour, or until a toothpick comes out clean. Cool in the pan for 30 minutes before removing from the pan. Invert onto a platter, plate, or cooling rack and continue to cool completely before frosting.

Using a whisk or a fork, in a medium bowl, mix powdered sugar, cocoa powder, and 2 tbsp rum.

Slowly add warm water until you get a drizzly consistency. It should be a very slow drizzle. If it is too thin, all the drizzle will end up on the plate and not on the top of the cake.

In a small saucepan, combine cocoa powder, sugar, and water.

Whisk over medium heat and bring to a simmer. Continue stirring for 3 minutes.

Remove from heat and stir in vanilla extract and 1 tsp rum. The sauce will thicken slightly as it cools.