Cruz’s mother, from what I have read, was a US citizen at the time of his birth. If his father had not officially renounced, (however one does that officially and legally) his Cuban citizenship, then he was a Cuban national. It hardly seems possible that he reamined “a man without a country” for decades, as he only naturalized as a US citizn in, I think, 2005.
And being born in Canada where his parents were living and continued to reside for 4 years, is also disqualifying.
Birth within the country assures no claims of allegiance by a foreign sovereignty, but it can be argued that those born “beyond the seas” could be regarded as natural born and in fact were for five years, from 1790 to 1795. Making any sort of attempt at a blanket acknowledgment proved problematic for some reason, and it seems reasonably clear to me that the problem was and is “ius soli” claims of sovereignty due to birth in a foreign nation. Not all foreign nations made that claim, and not all do today. If Canada didn't claim jurisdiction over Ted Cruz due to his having been born there, then there is no potential foreign legal interference or competition with his US citizenship.
If theses two situations were to be resolved favorably, I believe Ted Cruz is eligible. If there's a foreign claim due to either one, he's not.