Adam Clarke on Numbers 8:21

And Aaron made an atonement for them - Though the Levites had been most solemnly consecrated to the Lord's service, and though all legal washings and purifications were duly performed on the occasion, yet they could not approach God till an atonement had been made for them. How strange is it, after all these significations, of the will and purpose of God relative to man, that any priest or any people will attempt to draw nigh to God without an atonement! As sure as God hath spoken it, there is no entrance into the holiest but through the blood of Jesus, Heb 10:19, Heb 10:20.