It's beyond just requiring a special cleaning, it needs replacing. Yes, things do wear out, and this is an example of just that. The porcelain has chipped or rubbed off over the years, and no amount of cleaning will repair that because the finish is gone. The other option is to have it repainted. There are DIY kits for this, or you can have it done professionally. Personally, I'd replace it.

Ok, thanks so much for the helpful advise!

as a short term fix you can use something like CLR (calcium, lime, rust) remover. Leave it on for a little while to soak and then use an old toothbrush to scrub it. I usually have a couple of old toothbrushes in the cupboard for cleaning awkward little areas like this. It's the only thing that will get into these little crevices and if they get dirty it doesnt matter, I'll just toss it.

Im also wondering if it is actually rust since the drain looks like SS and doesnt appear to be rusting. It could also be calcium build up if you have hard water that has got stained but either way, the CLR will break it down.

Thanks for the tip. I have actually done that and it did take away some of the rust but still left the mold. Guess I will have to invest in a new sink.

I just saw the other post suggesting CLR. I have not tried that yet but will give it a shot. Thank you!

White distilled vinegar as well as a baking soda/water paste can kill mold and *may* take some of that coloring away.

Where is the rust coming from? The waste doesn't look like it's rusting (anyway, they're usually made of brass or stainless steel), so is it coming from the sink itself? Is your sink enamelled steel or cast iron? If it's the sink itself, the enamel has probably worn away from around the waste hole, allowing the steel to rust. I'd suggest removing the waste, and sanding down the area to remove the rust. Then you could treat with rust inhibitor (such as KuRust). Then once that's dry, paint the area with primer, allow to dry, then with new white enamel paint. Once that's thoroughly dry, you could blend it in with cutting paste, then re-install the waste with plenty of sealant. I don't think you can solve the problem by cleaning alone...

the sink is likely enamel over cast iron and the edge of the iron where the drain goes is exposed leading to rusting. Have you tried barkeeper's friend??

A pumice stone will take rust off. And not damage sink.

Another product which works very well is HG Rust Remover- if you can leave it to soak for a few hours, it works miracles. But you'd have to get the waste out first, and soak the rusty areas of the sink.. But do be careful not to get it on the enamel, as it may damage it.

HG Rust Remover

Thank you all for the comments and tips! I think the black looking area is actually permanently in the porcelain now so I am not sure if anything would remove it at this point. May just have to replace it.

I agree with lindac92, "the sink is likely enamel over cast iron" and that the enamel has worn off and the iron is rusting. We have a sink like that, and there a ways to inhibit the rust in the short time.But we have decided to replace the sink.