The word “Levites” here probably means priests Exodus 4:14, sons of Levi, since Bethshemesh was one of the cities of the priests Joshua 21:13-16. The burnt offering of the kine was not in any sense the offering of the men of Bethshemesh, but rather of the Philistine lords to whom the cart and the kine belonged. But the Bethshemites themselves, in token of their gratitude for such a signal mercy, now offered both burnt offerings and sacrifices, probably peace offerings, and doubtless feasted together with great joy and gladness (see 1 Kings 8:62-66; Ezra 6:16-17). There is nothing whatever in the text to indicate that these sacrifices were offered otherwise than in the appointed way by the priests.
Related Commentaries of 1 Samuel 6:15
1 Samuel 6:15
15 And the Levites took down the ark of the LORD, and the coffer that was with it, wherein the jewels of gold were, and put them on the great stone: and the men of Bethshemesh offered burnt offerings and sacrificed sacrifices the same day unto the LORD.