Preheat oven to 350 degrees F (175 degrees C). Spray 9 or 10 inch Bundt pan lightly with cooking spray and dust with flour.
In a medium bowl, combine flour, baking soda, salt, cinnamon, and allspice.
In a large mixing bowl, cream 1/2 cup butter, white sugar, and 3/4 cup brown sugar. Mix in eggs, 1/3 cup rum, and vanilla. Mix in flour mixture in three additions alternately with applesauce, ending with flour. Stir in dried cranberries. Spoon batter into prepared pan.
Bake in preheated oven for 45 to 55 minutes, or until a toothpick inserted into the cake comes out clean. Cool cake in pan for 15 minutes, remove from pan, and cool completely on a wire rack.
In a small saucepan, melt 3 tablespoons butter. Stir in 1/4 cup brown sugar, confectioners' sugar, and 2 tablespoons rum. Heat until smooth; if mixture is too thick, add water and maybe a little more rum. Drip glaze over cooled cake.