The water that leaks ends up on the floor?

Yes it's really hard to explain, but there must be corrosion inside the sink and it leaks out onto the floor. It doesn't leak around the drain so the water is traveling.

Does the sink leak with just 1" of water in it? Does it require several inches of depth before it leaks? Does it leak until it is completely empty?

You say the sink is cast iron. How did you decide that? Have you tested it with a magnet?

That sink is probably either soapstone or concrete with some sort of metal edge on top.

GOod point... I have no idea what it is made of. This is what my husband said :) It is extremely heavy which is why we thought it was cast.

It started leaking almost immediately and leaked until empty. The water didn't even make it to the edges of the sink, it went straight down the drain.

"some sort of metal edge on top."

Often lead.

I've seen some where the drain that's embedded in the concrete had corroded and created a leak. Maybe that's what you have going on. Can you see separate drains underneath or just one exit point in the center?

There is only one exit point, it's in the back corner of the sink. The leaking occurs at the front of the sink. You can see it dripping out there, which is why we think it's leaking into the sink bottom and then draining out.

There is a stamping on the front, what does it say?? That may shed some light on what its made of?