וַיֹּ֣אמֶר אֶֽל־אַהֲרֹ֗ן קַח־לְ֠ךָ עֵ֣גֶל בֶּן־בָּקָ֧ר לְחַטָּ֛את וְאַ֥יִל לְעֹלָ֖ה תְּמִימִ֑ם וְהַקְרֵ֖ב לִפְנֵ֥י יְהוָֽה׃
I rzekł do Ahrona: "Weźmiesz sobie cielca młodego na ofiarę zagrzeszną, i barana na całopalenie, zdrowe, i przywiedziesz je przed oblicze Wiekuistego;
Rashi
קח לך עגל TAKE THEE A CALF — This animal was selected as a sin offering to announce to him that the Holy One, blessed be He, granted him atonement by means of this calf for the incident of the golden calf which he had made (Midrash Tanchuma, Shmini 4)
Kli Yakar
Take for yourself a calf of the cattle for a sin offering. Some question why Aaron’s calf is brought as a sin offering while Israel’s calf is brought as a burnt offering. They explained that in the sin of the Golden Calf, Aaron did not sin in thought, as he certainly did not intend it for idolatry at all. His main sin was in the deed — that he actually made the calf, as it is written: And the Lord smote the people because they made the calf which Aaron made (Exodus 32:35). Why does it add which Aaron made? It comes to teach that Aaron sinned only in making the calf, but not in thought. Therefore his offering was a calf for a sin offering, which atones for sins of action. But Israel, who sinned also in thought, as they certainly intended it for idolatry, therefore their offering was a calf for a burnt offering, which comes to atone for sins of thought. What is difficult with this explanation is that Israel also sinned in deed, as they bowed down to it and sacrificed to it, so why didn’t they bring a calf as a sin offering for atonement? It seems to me that for the sin of sacrificing, they brought the goat for atonement, because it is said: And they shall no more sacrifice their sacrifices to demons (Leviticus 17:7). Where do we find that Israel sacrificed to goat-demons, that Scripture says no more? Rather, it certainly refers to what was said about the calf: and they sacrificed to it, because this sacrifice was certainly to goat-demons, to demons [that are] no-gods, as that entire incident was the work of Satan, and goat-demons dance there (Isaiah 13:21). Therefore it says, Take a young goat for a sin offering. But Aaron, who did not sacrifice to it at all, brought a calf as a sin offering to atone for making the calf.
Ramban
AND HE [Moses] SAID TO AARON: TAKE THEE A BULL-CALF FOR A SIN-OFFERING. Moses, our teacher, had been commanded about these offerings, as he said at the end [of the section], This is the thing which the Eternal commanded that ye should do,1Verse 6. although this [command for these specific offerings] is not expressly mentioned. Similarly, And Moses said: This is the thing which the Eternal hath commanded: Let an omerful of it be kept throughout your generations,2Exodus 16:32. [where the verse indicates that Moses received a Divine command although it is not specifically mentioned]. Also, I am the G-d of Beth-el,3Genesis 31:13. when Jacob related [to his wives all that G-d’s angel had told him in the dream], even though it is not mentioned in Scripture that he was so told. I have already shown to you4Exodus 11:1. Also ibid., 12:21. many such examples in the sections on the commandments regarding the Passover.