In a large mixing bowl, combine flour, sugar, baking powder, salt, butter, and 3 tablespoons oil. On low speed combine ingredients until the mix is the consistency of cornmeal.
Spray or oil a large Bundt pan and sprinkle the chopped walnuts on the bottom evenly.
To the dry mix add the pudding mix, milk, eggs, rum, 1/2 cup oil, and vanilla extract.
Combine on medium speed with electric mixer for 2 to 3 minutes, scrape down the bowl halfway through, until the batter is very smooth. Mix in the coconut quickly with the mixer.
Pour into Bundt pan and bake for about 55 minutes- until fully golden and tester comes out clean and cake springs back. Remove from oven and place on a cooling rack.
Rum Soaking Glaze
Combine butter, water and sugar in a small saucepan. Bring to a boil slowly and reduce to a simmer until sugar is dissolved and syrup is a little thicker. Remove from the heat and add the rum and vanilla, mix to combine.
Pour a little bit of the hot syrup at a time on top of the cooling cake, allowing it time to soak in. Continue until all of the syrup is added.
Cool and leave in pan overnight covered. Turning cake out gently onto a serving plate.