Preheat oven to 325 degrees F (165 degrees C). Grease and flour a 10 inch tube or Bundt pan. Sprinkle nuts over the bottom of the pan.
Mix together the cake mix, 1/2 cup dark rum, eggs, 1/2 cup water, oil, and vanilla pudding mix. Pour batter over the nuts in the pan.
Bake for 45 minutes to 1 hour. Cool, and invert cake on a serving plate. Prick the top of the cake with toothpicks.
To Make The Glaze: Melt the butter in a saucepan. Stir in 1/8 cup water and the 1/2 cup sugar. Boil for 5 minutes, stirring constantly. Remove glaze from heat, and stir in 1/4 cup rum. Drizzle and smooth evenly over the top and sides.