As an American citizen you are required to the follow the laws of the USA despite any other nationality that you may have. Most laws don't apply to citizens residing abroad, but some do. Perhaps the most significant is paying taxes on world-wide income, but also includes participating in the selective service (military draft), reporting foreign bank account balances and respecting embargoes on various countries. There also some recent laws which involve restrictions and punitive measures for US citizens engaging drug use, trading in pirated merchandise, or sexual activities with minors abroad, even when these practices would not violate laws in the country where the event happened.
Regarding Cuba, specifically the official regulations state:
They apply to all persons (individuals and entities) subject to U.S. jurisdiction –
including all U.S. citizens and permanent residents wherever located, all
persons in the United States, and all branches and subsidiaries of U.S.
organizations throughout the world – as well as all persons engaging in
transactions that involve property in or otherwise subject to the jurisdiction
of the United States.
Unless authorized by a general or specific license, any person subject to U.S.
jurisdiction who engages in any Cuba travel-related transaction violates the
Regulations and may be subject to penalties.
In reality if you are not living in the USA and have no substantial contact such as bank accounts, residence, etc. nothing will probably happen, but it is not strictly legal.
EDIT: This post goes into more details:
Are there any US laws that a US citizen MUST obey while traveling, even if those laws do not exist in the country he is traveling to?