Preheat the oven to 350 degrees F (175 degrees C). Grease and flour a Bundt pan.
Beat together cake mix, pudding mix, water (or coffee), oil, eggs, ½ cup Kahlúa, and vodka in a large bowl until smooth and light, about 4 minutes.
Transfer the batter to the Bundt pan. Cook in the preheated oven until a toothpick comes out clean, 45 to 50 minutes.
Let the cake cool, then flip out onto a plate or cake stand. Let sit 20 minutes before glazing.
Make the glaze: Whisk together confectioners' sugar, milk, and 1 tablespoon Kahlúa in a small bowl. Spoon over the crest of the cake and allow it to dip down the sides.
