Preheat oven to 325°F (165°C). Grease and flour a 10-inch bundt pan or two loaf pans.
In a large bowl, cream together the softened butter, vegetable oil, and 3 cups of sugar until light and fluffy.
Add eggs one at a time, beating well after each addition.
In a separate bowl, sift together flour, baking powder, and salt.
Alternately add the dry ingredients and milk to the creamed mixture, beginning and ending with dry ingredients; mix just until combined.
Stir in the coconut, rum, butter, lemon, and vanilla extracts until fully incorporated.
Pour the batter evenly into prepared pans and smooth the top.
Bake in preheated oven for 55-65 minutes, or until a toothpick inserted in the center comes out clean.
While the cake bakes, prepare the almond syrup: combine water, 1 cup sugar, and almond extract in a small saucepan over medium heat; stir until sugar dissolves and syrup is slightly thickened, about 5 minutes.
When cake is done, remove from oven and allow to cool in pans for 10 minutes before inverting onto a wire rack.
While the cake is still warm, poke holes all over the top with a skewer and brush the almond syrup evenly over the cake to soak in.
Let cake cool completely before slicing and serving for best flavor and moisture.