But we know a lot about the ancestry of the US presidents, and so far as I know, genealogists haven't really been able to connect any of them with Indian ancestors, though claims were made for Coolidge and Clinton and the Bushes.
Charles Curtis, Hoover's vice president actually was an Indian, though, and Rick Perry is supposed to be part Choctaw.
We don't know just how Cherokee Warren's ancestor is supposed to be. That great-great-great-grandmother may have been a member of the tribe but have been only partly of native American ancestry herself.
Somebody may be able to double check that ancestor (Sarah Smith) at a US census records or genealogical website.
Supposedly, all of them except Martin Van Buren (Dutch) can trace their ancestry back to King John I of England. Not that is necessarily something to be proud of. John I was a lout of the first order who sired scores of illegitimate children.
Native American connections are a lot tougher to document because most of them took on English names when they married. The more famous like Pocahontas whose descendants include the Byrd and Bolling political families are the exception, not the rule.
Charles Curtis, of course, was a gentleman of the first order and proud of his Native American heritage. His public service, of course, dates to a time where Native Americans were finally granted the vote and full citizenship, a full generation or more after slavery was abolished.
The Bush family, of course, dates back to the earliest days of the Massachusetts Bay Colony. I believe their Native American heritage is fairly well documented back to the earliest days of the colony by multiple New England genealogists including this guy.