There are 2 US Post Offices in Cumberland County serving a total of 6,558 residents equating to 3,279 residents per post office. It's estimated that approximately 10,467 packages are handled across the 2 county post offices annually. Cumberland County is a county located in the U.S. state of Kentucky. As of the 2010 census, the population was 6,856. Its county seat is Burkesville. The county was formed in 1798 and named for the Cumberland River, which in turn may have been named after the Duke of Cumberland or the English county of Cumberland. Cumberland County was a dry county however now is a wet county as of June 28, 2016, which means that the sale of alcohol is now legal.