Preheat your oven to 350 degrees.
Grease and flour your desired bundt pan. Set your baking pan aside.
To a stand mixer or large bowl, add the flour, sugars, baking powder, salt and butter
On low speed, combine ingredients until the mix is the consistency of fine gravel, and all particles are about the same size.
If your coconut oil is solid, heat the oil until just melted and liquid in your microwave. Be sure that it's not too hot and it's just melted.
Then and to the flour mixture the pudding mix, coconut milk, eggs, rum, coconut oil, coconut extract and vanilla extract and combine on medium speed for 2 to 3 minutes, be sure scrape down the sides of the bowl halfway through.
Fold in the shredded coconut into the cake mix .
Pour the batter into your prepared bundt cake pan.
Bake for about 55 minutes- until fully golden and tooth pick comes out clean.
Remove from oven and place on a cooling rack while making the soaking rum glaze.
Once your cake is completely cooled, using a wooden skewer, poke the entire cake to ensure the rum soaks the cake as much as possible.
Prepare your rum glaze by combining butter, rum, water and sugar in a small saucepan over medium heat. Bring to a boil to ensure all of the sugar is dissolved.
Once the sugar has completely melted into the syrup, remove from the heat and slowly pour it into the cake inside the cake pan.
After you've poured all the rum sauce onto the cake and it's been completely absorbed, carefully flip the cake pan onto a serving dish.