Put the sugar and water in small saucepan over high heat. Gently stir just until the sugar has dissolved. Cook until the mixture without stirring until it turns a deep amber color.
Off the heat immediately add the heavy cream, the mixture may rise up (we recommend wearing an oven mitt) Return the pan to the stove and cook over medium heat until the sauce thickens about 3 to 5 minutes.
Off the stove mix in the butter and rum until the sauce is thick and shiny. Serve immediately or store in the refrigerator. To reheat the sauce, simmer gently over low.