Cuba, IndianaCuba is an unincorporated town in Springfield Township, Allen County, in the U.S. state of Indiana. Cuba Mennonite School is located here, as is the Cuba Mennonite Church.HistoryCuba was platted in 1855. It was named after the island nation of Cuba.GeographyCuba is located on Highway 37, also known as Maysville Road. Cuba Road extends north from Cuba, and Thimlar Road extends to the south.