Square Lake is an unorganized territory in Aroostook County, Maine, United States. The population was 706 at the 2020 census. According to the United States Census Bureau, the unorganized territory has a total area of 414.4 square miles, of which 382.8 square miles is land and 31.6 square miles, or 7.63%, is water. There are several lakes in the unor…Square Lake is an unorganized territory in Aroostook County, Maine, United States. The population was 706 at the 2020 census. According to the United States Census Bureau, the unorganized territory has a total area of 414.4 square miles, of which 382.8 square miles is land and 31.6 square miles, or 7.63%, is water. There are several lakes in the unorganized territory, including the eponymous Square Lake as well as Eagle Lake, Cross Lake, and Mud Lake.