Charles Ellicott Commentary 1 Chronicles 11:8

"And he built the city round about, from Millo even round about; and Joab repaired the rest of the city." — 1 Chronicles 11:8 (ASV)

And he built the city round about. —Literally, and he built (or rebuilt or fortified) the city all around, from the Millo even to the complete circuit.

The Millo was probably a tower or citadel, like the Arx Antonia of later times. According to the chronicler, David started from that point and brought his line of defenses around to it again. Samuel simply states, And David built around, from the Millo, and inward. This seems to mean that he carried his buildings from the fortress towards the interior of the city. Both statements may, of course, be true.