2 Samuel 8:18 Benaiah son of Jehoiada was over the Kerethites and Pelethites; and Davids sons were royal advisers [NIV note reads, priests].

The Hebrew test reads "priests." David may be being viewed as a priest-king along the lines of Melchizedek, who was king of Salem and priest of God most high (Gen. 14:8; Psa. 110:4). Another solution may be to see this through the eyes of the parallel phrase in 1 Chronicles 18:17 (chief officials at the king's side). Therefore, here David's sons would be stewards. The New American Commentary states:

Davids sons served as priests (Hb. kōhănm; NIV, royal advisers). Scholars have proposed various explanations of the actual role Davids sons played as priests. Some, such as the NIV, take their interpretive cue from 1 Chr 18:17 and translate the term kōhănm as though it conveyed a consultative role. G. J. Wenham proposes a textual emendation and suggests they were administrators of the royal estates. It is preferable, however, to interpret the term in light of Davids presumed status as a priest in the order of Melchizedek (cf. comments on 6:14); accordingly, Davids sons would have possessed the inherited title and performed whatever duties were associated with the office. Still others understand the term to refer to Davids sons participation in sacerdotal duties that could be performed by laypersons. Although I know of no scholar who holds this position, a fourth - and unlikely - possibility is that David bestowed the title on his sons in recognition of the Torahs assertion that Israel was to be a kingdom of priests (Exod. 19:6): as a faithful son of the covenant, David was a priest, and by bestowing the title on his sons, he was dedicating them to faithful service to the covenant as well.

Reference

Bergen, R.D. The New American Commentary Vol. 7, 1, 2 Samuel. In Logos Library System electronic ed. Nashville: Broadman & Holman Publishers, 2001.