Bede

After him Nehemiah built, etc. Note that King David is buried not in Bethlehem, as some assert, but in Jerusalem; and indeed not without a certain reason of mystery. For just as in Bethlehem he was born and anointed as a king, prefiguring that the Lord Christ would be born there from his seed and be adored by the Magi under the guise of a king; so also, having died and been buried in Jerusalem, he signified that the same Lord would suffer and be buried in that city, but would rise again from the grave. …

Commentary on Ezra and Nehemiah ↗