2 Samuel 5:9

So David dwelt in the fort, and called it the city of David. And David built round about from Millo and inward.

David lived in the stronghold, and called it the city of David. David built round about from Millo and inward.

And David dwelt in the stronghold, and called it the city of David. And David built round about from Millo and inward.

And David dwelleth in the fortress, and calleth it -- City of David, and David buildeth round about, from Millo and inward,

So David took up residence in the fortress and called it the City of David. He built it up all the way around, from the supporting terraces inward.