Heat oven to 350°F (175°C), grease and flour a 9x5-inch loaf pan.
Beat softened butter with sugar until light and fluffy (3–4 minutes).
Add eggs one at a time, mixing well after each addition.
Stir in mashed sweet potatoes, coconut milk, and dark rum until combined (batter may look curdled).
Sift flour, baking powder, baking soda, and salt. Add gradually to the wet mixture, mixing just until combined.
Pour batter into the pan, smooth the top, and bake for 55–65 minutes until golden and a toothpick comes out clean or with moist crumbs.
Cool in the pan for 10 minutes, then transfer to a wire rack. Slice and serve (dust with powdered sugar if desired).