Preheat the oven to 350°F. Generously grease and flour your 10-inch bundt pan.
Combine the cake mix, pudding mix, water, eggs, rum, and oil in a large bowl.
Beat the mixture on low speed for 30 seconds. Increase to medium speed and beat for 2 minutes.
Gently fold in the drained crushed pineapple. Transfer the batter into your prepared pan.
Bake for 45 minutes. A toothpick inserted into the center should come out clean.
Cool the cake in the pan for exactly 15 minutes. Then, carefully invert it onto a wire rack.
Mix 1 cup of confectioner's sugar with the pineapple juice in a small bowl. Brush this glaze over the warm cake. Let the cake cool completely.
Combine the remaining sugar, rum, and cream of coconut in a separate bowl. Drizzle this over the cooled cake and sprinkle with shredded coconut.