Grease and flour a 10-inch Bundt pan. Sprinkle walnuts on the bottom of the pan. Preheat the oven to 325 degrees F. Mix together cake mix, pudding, oil, 1/2 dup rum, eggs and 1/3 cup of cold water in a mixer on low speed for 6 minutes. Pour batter over walnuts.
Put cake in the oven for 1 hour till clean through testing with a toothpick or fork. When the cake is done, let it cool for 1 hour.
For the frosting mix 1/4 cup of water, sugar, 1/2 cup of rum, and butter. Let it boil in a pan for 5 minutes. Then pour it all over on top of the cooled cake.