Preheat oven to 350°.
To prepare cake, coat an 8 x 4 inch loaf pan with cooking spray; dust with 2 tablespoons flour.
Lightly spoon 1 1/2 cups flour into dry measuring cups; level with a knife. Combine 1 1/2 cups flour, baking powder, baking soda, and salt, stirring with a whisk until blended.
Place granulated sugar and butter in a large bowl; beat with a mixer at medium speed until well blended (about 5 minutes). Add eggs, 1 at a time, beating well after each addition. Add flour mixture and 1/2 cup rum alternately to sugar mixture, beginning and ending with flour mixture. Spoon batter into prepared pan. Bake at 350° for 50 minutes or until a wooden pick inserted in center comes out clean. Cool in pan 10 minutes on a wire rack. Run a knife around edges of pan; remove cake from pan. Cool completely on wire rack.
To prepare glaze, combine powdered sugar and 1 1/2 tablespoons rum, stirring until smooth. Drizzle glaze over the cake.