Yes. U.S.-Cuban dual citizens are permitted to arrive in Cuba by vessel. If you are a U.S.-Cuban dual citizen, you will need additional documentation.
U.S.-Cuban dual citizens who departed Cuba on or after January 1, 1971 must enter Cuba using their Cuban passport book. Such persons must use their U.S. passport book to enter and depart the United States. They do not need a visa, however they do need a Cuban passport habilitation and two completed copies of the Travel Certification Document. Please refer to the U.S. Embassy in Cuba website for more information.
U.S.-Cuban dual citizens who departed Cuba prior to January 1, 1971 must travel to Cuba with their U.S. passports valid for at least 6 months after the date of Cuba sailing. They also need two completed copies of the Travel Certification Document and a special type of visa, which they need to apply for prior to travel.
Royal Caribbean does NOT administer the type of visa required for U.S.-Cuban dual citizens who departed Cuba prior to January 1, 1971. There are several companies that offer visa/passport processing services to assist in obtaining a visa and/or a Cuban passport including: