One part of the law states:
Operations to Cuba.
No person may operate a civil aircraft from the United States to Cuba unless--
(a) Departure is from an international airport of entry designated in Sec. 6.13 of the Air Commerce Regulations of the Bureau of Customs (19 CFR 6.13); and
(b) In the case of departure from any of the 48 contiguous States or the District of Columbia, the pilot in command of the aircraft has filed--
(1) A DVFR or IFR flight plan as prescribed in Sec. 99.11 or Sec. 99.13 of this chapter; and
(2) A written statement, within 1 hour before departure, with the Office of Immigration and Naturalization Service at the airport of departure, containing--
(i) All information in the flight plan;
(ii) The name of each occupant of the aircraft;
(iii) The number of occupants of the aircraft; and
(iv) A description of the cargo, if any.
This section does not apply to the operation of aircraft by a scheduled air carrier over routes authorized in operations specifications issued by the Administrator.
Now admittedly you'll be flying under Part 135 for renting a private jet but similar provisions apply.
I'll give you one guess at your likelihood of getting a special authorisation to fly to Cuba is.
You can get there - but you would have to land in another country first.