What city is called the city of david?

Two cites in The Bible are know as the city of David. The first was a Canaanite city which David captured and renamed it City of David in his 6th year of his reign, later it was renamed Jerusalem. The second city in the Bible was Bethlehem, here Jesus was born. It was called that because King David's reign was forever (in Christ) or the everlasting kingdom which was established by Christ at David's anointing by Samuel. Source is found in Psalms.