A natural born Citizen is a person who at birth has no foreign sovereignty laws that govern his Citizenship. Cruz is a statutory Citizen and was never eligible to be an Article 2 Section 1 natural born Citizen at birth due to his foreign national father and his birth in a foreign sovereigty. Natural born Citizens never have to renounce foreign citizenships.
No, a natural born citizen is one who was an American citizen at birth, as opposed to naturalizing later. Cruz is certainly that.
Since Cruz was born abroad, he is a Citizen by statute. He is not a natural born Citizen born within the jurisdiction of the United States. Again, the principal framer of the 14th Amendment Representative John Bingham explained the founders original intent defining a natural born Citizen.
“Every human being born within the jurisdiction of the United States
of parents not owing allegiance to any foreign sovereignty is, in the language of your Constitution itself, a natural born citizen.” (Cong. Globe, 39th, 1st Sess., 1291 (1866))
Cruz's father Rafael owed allegiance to Cuba
Barack Obama Sr. owed allegiance to Great Britain.