Cosby is a census-designated place and unincorporated community in Cocke County in the U.S. state of Tennessee. The population of the Cosby CDP according to the 2020 census was 807. The community has given its name to the northeastern section of the Great Smoky Mountains National Park, which forms its southern boundary. Cosby's zip code also exte…Cosby is a census-designated place and unincorporated community in Cocke County in the U.S. state of Tennessee. The population of the Cosby CDP according to the 2020 census was 807. The community has given its name to the northeastern section of the Great Smoky Mountains National Park, which forms its southern boundary. Cosby's zip code also extends to into Sevier County, and borders the town of Pittman Center.