You can try bleaching the black stains but you need to sand the finish off, first, to get down to the bare wood where the black stain has penetrated, then you will have to reapply the finish and any wood stain to match the rest of your flooring. (you may have a stain applied to the floors to make them different than their natural color, plus a protective coat of wax, polyurethane or another type of finish. To match the rest of the floor you will need to find out what you have to restore the floor's appearance after you get the black stains up). If you google "bleach hardwood floor stains" several articles will pop up, including the one I've linked to below.

If you post a pic, I'm sure you'll get some other opinions as well. Good luck!

Here is a link that might be useful: black stain removal