Position rack in center of oven and preheat to 325 degrees F. Spray a 10-inch (12-cup) bundt pan with nonstick spray.
Using an electric mixer, beat cake mix, rum, vegetable oil, pudding mix, and eggs in a large bowl for 2 minutes. Transfer batter to prepared pan.
Bake until a toothpick inserted in center of cake comes out clean, about 45 minutes. Cool cake in pan for 20 minutes. Invert cake onto platter, then carefully remove pan. Allow cake to cool completely.
Rum Glaze Preparation:.
Meanwhile, stir sugar and water in a heavy medium saucepan over medium high heat until sugar dissolves. Add butter. Simmer until mixture thickens and is syrupy, stirring often, about 5 minutes. Remove saucepan from heat and whisk in rum. Cool glaze completely. Drizzle glaze evenly over cooled cake and serve.