Preheat oven to 350° F . In a large mixing bowl beat butter with an electric mixer on medium to high speed for 30 seconds. Add sugar, about 1/4 cup at a time, beating until combined. Add eggs, one at a time, beating well after each addition. Beat in vanilla. Alternately add flour mixture and coconut milk to butter mixture, beating on low speed after each addition just until combined. Fold in the 3/4 cup coconut and the rum.