Preheat oven to 350ºF. Grease a Bundt pan.
In a large mixing bowl, combine the red velvet cake mix, instant chocolate pudding mix, sour cream, eggs, water, and oil. Mix with a hand mixer or whisk just until combined and smooth.
Pour the batter into the prepared Bundt pan. Bake 45-55 minutes, or until a toothpick inserted into the center comes out clean.
Cool for 10 minutes, then invert the cake onto a cake plate. Allow the cake to cool completely before frosting.
For the icing, in a mixing bowl, beat together the softened cream cheese and butter with a hand mixer or spatula until creamy and smooth. Add powdered sugar and vanilla, and mix again until smooth.
Fill a pastry or Ziploc bag and cut off the corner. From the outside in, squeeze and pull a line of frosting up and over the cake, into the center hole. Repeat around the whole cake.