I don’t if that is Kosher but there are brands of rum that have an OU. I have been searching for a brand of rum that has a Heimisher hechser and have not yet found. Spirits of Solomon does not make. If any one knows of a brand of with a heimisher hechser please let me know my wife wants to make rum cake.
Rum can be seriously not kosher it usually won’t have a hechsher on the bottle but if you dont see it on a list of approved liquors then dont drink it.
RebRY, hechsherim are not my area of expertise, but i can help your wife out a little with baking. If she wants to make a rum cake & has no rum, she can substitute vodka, same amount as rum in the recipe, and a teaspoon (or a teaspoon and a half for stronger flavor) of good quality rum flavoring.