Preheat oven to 350 F.
Generously coat Bundt pan with cooking spray; set aside. Whisk together flour, baking powder, baking soda, and salt in a large bowl. Set aside.
Beat butter, sugar, and vanilla on medium speed in a stand mixer with a paddle attachment until light and fluffy (about 4 minutes).
Add eggs, one at a time, beating well and scraping down the bowl after each addition.
Reduce mixer speed to low and gradually add the rum.
Add flour mix in three parts, alternating with the heavy cream, beginning and ending with the flour.
Pour batter into Bundt pan, smoothing the top of the cake.
Bake in preheated oven until golden brown (roughly 60-75 minutes, but may depend on your bundt pan so check early and often!). A toothpick inserted in the center should come out clean, and the sides of the cake should begin to peel away from the pan. If the top of the cake begins to brown excessively, cover with tin foil.