These were the sons of Levi after their fathers' houses, even the heads of the fathers' [houses] of those of those who were counted, in the number of names by their polls, who did the work for the service of the house of Yahweh, from twenty years old and upward.
Here is the complete frustration of the efforts of radical critics to late-date the Pentateuch.  And, as for the allegation that some late Chronicler falsely attributed all these words and activities to King David, such a theory is just as unreasonable and impossible of acceptance as would be the allegation of some alleged `scholar' someone named Smith or Brown discovered America instead of Christopher Columbus.