There is an "F" used in the 1851 census in the birth place column but it refers to the person being born of Canadian parents. So if you see CW F it means born in Canada West of Canadian parents.
It would be Solomon P. Cook married to Cordelia (Parker) Cook. In it looks like they lived next to or with Cordelia's parents, Nancy and James Parker.
Attached is a copy of the record. Solomon is my sticking point. I can find him in the 1861 census listed as a saloon keeper. I can not find his birth or death records.
In 1851 he was in ?? don't remember, I'll have to recheck some records, but in 1861 he was in Cayuga.
Thanks for u/l the image. It just means what I said in my first answer - born in Canada West of Canadian parents.
Not all of 1861 has survived and not all that has survived has been uploaded on Ancestry.com (they have a little note about this in the info on the census which appears at the bottom when you are searching)
So don't give up, it may be that Solomon's location images just aren't online yet!