Preheat oven to 350 degrees F ( 175 degrees C). Grease and flour a 10 inch fluted or tube pan.
In large mixing bowl, combine cake mix, pudding mix, 1/2 cup coconut creme, 1/2 cup rum, oil, and eggs. Beat with an electric mixer on medium speed for 2 minutes. Stir in pineapple. Pour into prepared pan.
Bake for 50 to 55 minutes. Cool 10 minutes. Remove from pan. With a table knife or skewer, poke holes about 1 inch apart in cake almost to bottom.
Combine remaining coconut creme and 2 tablespoons of rum. Slowly spoon over the cake. Chill thoroughly. Store in refrigerator.