Combine the cheese and rum in a fondue pot set over low heat. Heat until the cheese is melted and the mixture is blended, stirring constantly. Add the chocolate and heat until blended, stirring constantly. Stir in the espresso and sugar. If substituting coffee granules for the espresso, dissolve the granules in 3 tablespoons hot water before adding to the fondue pot. Keep fondue warm over low heat.
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