Based on my research, Cruz would be eligible to be a Cuban citizen if his father filed application for it. I doubt that ever happened.
http://www.cubanet.org/htdocs/ref/dis/const_92_e.htm
Chapter II
Article 29c
The Constitution has a reference to person born overseas of at least one Cuban citizen, but the Constitution says you have to comply with the stipulations of law.
Cuba, being a communist country, is not happy with dual-U.S./Cuban citizens.
Dual Nationality: The Government of Cuba does not recognize the U.S. nationality of U.S. citizens who are born in Cuba or are the children of Cuban parents. These individuals will be treated solely as Cuban citizens and may be subject to a range of restrictions and obligations, including military service. The Cuban government may require Cuban-American citizens to enter and depart Cuba using a Cuban passport. Using a Cuban passport for this purpose does not jeopardize one’s U.S. citizenship; however, such persons must use their U.S. passports to enter and depart the United States. In some instances, dual nationals may be required to obtain exit permission from the Cuban government in order to return to the United States. There have been cases of Cuban-American dual nationals being forced by the Cuban government to surrender their U.S. passports. Despite these restrictions, Cuban-American dual nationals who fall ill may only be treated at hospitals for foreigners (except in emergencies). See the Consular Access paragraph below for information on Cuba’s denial of consular services to Cuban-American dual nationals who have been arrested, as well as the Children’s Issues paragraph below for information on how dual nationality may affect welfare inquiries and custody disputes.
>funny, isn’t it, that you thought a communist country would recognize a person to be a dual citizen by birth, but not a democratic country.