Stain removal in marble sink

Try making a paste with white vinegar and baking soda,cream of tartar and lemon juice or hydrogen peroxide and cornstarch

If you can't get rid of it, may be make a feature of it. eg: Stick something like Glass Pebbles with Waterproof Sealant around it. They come in many colours...............

Try soaking it with water and bleach

Here are some suggestions. I would skip the vinegar one though, since it can pit or etch marble and cultured marble.

http://tipnut.com/marble-granite-stains/

This is not a commercial, but our painter told us about BioClean. Ace Hardware stores carry it sometimes, but also on Amazon. Amazing Stuff! It removed rusted nail spots on 115 year old house of ours, all hard water spots on brass bathroom fixtures and is environmentally safe. Is safe for granite-made my countertops shine. It is green in color and there is a picture of a lady and a little girl on the label. It is definitely worth the money.

Try "The Works" from Wallmart.

This is not a commercial, but our painter told us about BioClean. Ace Hardware stores carry it sometimes, but also on Amazon. Amazing Stuff! It removed rusted nail spots on 115 year old house of ours, all hard water spots on brass bathroom fixtures and is environmentally safe. Is safe for granite-made my countertops shine. It is green in color and there is a picture of a lady and a little girl on the label. It is definitely worth the money.

rub with Lava soap bar

YouTube has a lot of ideas: https://www.youtube.com/results?search_query=how+to++get+stains+out+of+cultured+marble+sink

Mineral Oil (Baby oil) and a soft cloth. You may have to repeat a few times to get it all off. Then clean the whole sink with the mineral oil regularly to seal it and keep it from staining again.

my housekeeper had me get her "maintex" shower, tub and tile cleaner. works on hard water spots

pumice stone. I buy at Home Depot

TLC sold at pool stores. It cleaned the rust off our pool slide and the years of build up from well water in our toilet making it bright white like new.

Sanitizing tablets for baby bottles. put in sink with enough water to cover stain and leave overnight. Worked for me.

Try a mr clean magic eraser

WOW! All great solutions. I am going to read them all again and see which works best. Am tired of these stains in my sinks.

Try this: https://www.amazon.de/Meiko-Melaminschwamm-Schmutzradierer-wei%C3%9F-St%C3%BCck/dp/B004304DQK