In a medium bowl, combine the flour, baking powder, and the salt. Stir well.
Using a hand mixer, cream the butter and sugar in a large bowl. Add the eggs, one at a time, and mix thoroughly well. Add alternately the flour and the milk, ending with the milk. Add the lime juice, lime zest, the rum and vanilla extracts. Mix well, using a spatula. Pour the batter into a well greased and floured baking pan, cake pan, bundt pan, or tube pan.
Bake at 375 for about 45-55 minutes. Allow the cake to cool for at least an hour.
To make the glaze, using the stove and a medium sauce pan, melt the butter and sugar together. Stir well until melted. Add the lime juice, zest, and the extracts. Pour the warm glaze over the cake. You may also add sifted powdered sugar, or omit the glaze and garnish with just the powdered sugar. Enjoy!