- 431 “The stubble of several nights”
- 3 “several nights' stubble”
- 1,510 "several days' beard growth"
As a native speaker from the middle of the country and a lawyer with high verbal scores, I can tell you I have never heard either one used. I have added a third choice that I have heard and used myself. All are technically correct but usage may vary.
If you've seen the first two in print, then either they were used at one time or are used in one of the bazillion places where native speakers accumulate local uses (though narrowed down to places where they publish such books and think they are the model which leaves only New York & London). The true native speakers, the rural south England peasantry, are not common I don't think. Their descendants, the urban south England working class, are unintelligible to outsiders often intentionally.
Thus, there remain two traditional ways to speak English, (1) one is Received Pronunciation that is the usage of the British upper classes as taught in the private "Public" boarding schools, and (2) General American which is used in an area extended a modest ways from Omaha. There are others, (3) NBC English, (4) BBC English, MLA, etc. If you want to use it like an American, read and reread Strunk & White and an out of date Harbrace College Handbook.
Remember that what colleges teach today is politically correct and offensive to 80% of the country. If you want to hear Standard American, listen to Johnny Carson or Warren Buffet. Both are from Nebraska and hit the sweet spot. If an English book was written in the US in the last year, it was written to please people that hate America and see English as one more tool to sell Marxism. They've butchered it, and their influence will pass.