'City of David' in the Bible

But the gate of the fountain repaired Shallun the son of Col-hozeh, the ruler of the district of Mizpah; he built it, and covered it, and set up the doors thereof, the locks thereof, and the bars thereof, and the wall of the pool of Shelah by the king's garden, and unto the stairs that go down from the city of David.

And at the fountain gate, which was opposite them, they went up by the stairs of the city of David, at the ascent of the wall, above the house of David, even unto the water gate eastward.