"Cuba" is a Sicilian derivation of the Arabic Ka'aba, meaning "cube" or "square-shaped structure," which is the shape of this building. Built in 1180 by King William II, it was a kind of summer palace, or sollazzo, with vast royal gardens where the court came to escape the heat. A tall building with a rectangular plan, it is a magnificent piece of Fatimid architecture. The interior of the original structure had a hall that rose the full height of the building and was covered by a dome.
Giovanni Boccaccio made La Cuba a setting in his tales of The Decameron. After it fell from royal use, it was privately owned, becoming a leper colony. While you're there, make sure to pop into the Punic Necropolis next door.