Cuba City is a city partially in both Grant County and Lafayette County in the U.S. state of Wisconsin. The population was 2,086 at the 2010 ce…Cuba City is a city partially in both Grant County and Lafayette County in the U.S. state of Wisconsin. The population was 2,086 at the 2010 census. Of this, 1,877 were in Grant County, and 209 were in Lafayette County. The city is nicknamed "The City of Presidents" because of the presidential banners displayed along the city's Main Street.