There are 6 US Post Offices in Cocke County serving a total of 36,738 residents equating to 6,123 residents per post office. It's estimated that approximately 58,638 packages are handled across the 6 county post offices annually. Cocke County is a county in the U.S. state of Tennessee. As of the 2010 census, the population was 35,662. Its county seat is Newport. Cocke County comprises the Newport, TN Micropolitan Statistical Area, which is part of the Knoxville-Morristown-Sevierville, TN Combined Statistical Area."