No. The United States does not own any territory in Cuba. Cuba has been a fully independent nation since 1902 (formally from 1903 after the Platt Amendment era).
Common confusion point: The U.S. has leased Guantánamo Bay Naval Base since 1903 under a perpetual treaty—but this is a leasehold, not sovereignty. Cuba disputes the lease's legitimacy and refuses to cash the annual rent checks. The base remains a unique geopolitical anomaly, but Cuban territory it remains.