He resided in Cambridgeville, now Newton, Mass., 1665-1690.
He was a shoemaker.
m2. Nov. 1681 widow Susanna Goodwin.
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If we are talking about someone being born in what is now Massachusetts in 1621, we are talking about the Mayflower and "The First Thanksgiving" kind of history. There is not much from that period that has escaped notice. There was a Cooke on the Mayflower, Francis Cooke, but there is no record of him having a son, Gregory. Certainly not on the first year he was there.
What is now Newton, MA was settled in 1630 as a part of "the new town" and renamed Cambridge in 1638 and renamed Newtown in 1691 and Newton in 1766. (ref. Wikipedia, aka "The Font of all Knowledge.") Gregory Cooke was certainly one of the earliest residents of Newton, but it is doubtful that he was born there. If he had been, it could not have been prior to 1630. If he was born in Massachusetts in the 1620s, it probably would have been something that would have gotten a lot of attention in any written history of the Cooke family in America. It is more likely that he was born in England and came to America as a young man.
My recommendation is to change his date and place of birth to something like, "about 1630" and "England (uncertain)".