How To Remove Scuff Marks From Vinyl Floor?

I use a mild soapy liquid and a nylon "scrubby" pad VERY gently to get it started, then I use a cloth towel to rub the rest off.  I've also used diluted Fantastic cleaner to try and lift it.  
Hope that helps.
Moe

I stored a spare tire in my RV by laying it on the linoleum floor. Over time the tire left a round dark mark on the floor. I have tried Soft Scrub and a cleaner with bleach but can't get the entire mark off the floor. What else could I use?

You can use soft scrub or goof off.