Preheat oven to 325°F. Grease and flour 10-inch tube or 12-cup bundt pan. Sprinkle nuts over the bottom of pan. Mix the cake mix, instant pudding, eggs, water, dark rum and oil together. Pour batter over the nuts and bake for 1 hour. Set aside to cool. After cake has cooled, invert on a serving plate and prick top.
Melt butter in a saucepan. Stir in water and sugar. Boil for 5 minutes. Stirring constantly. Remove from the heat and stir in the rum. Drizzle and smooth glaze evenly over the top and sides of the cake. Allow cake to absorb the glaze. Repeat until glaze is used up.