So “Aaron drew near unto the altar,—and slew the sin′-bearing′ calf、 which was for himself;” (Lev 9.8, EMPH)

The Emphasize Bible has an interesting translation of the words in bold here. In the ESV this same expression is translated calf of the sin offering.

The Hebrew word means: “sin, transgression, sin offering, punishment…It also implies an antidote to sin, including purification from ceremonial impurity (Num. 19:9, 17); the sacrificial offering for sin (Ex. 29:14; Lev. 4:3); and the punishment for sin.” [Complete Word Study Bible]

I like the way The Emphasized Bible translates the term because it captures the essence of what is going on in the offering. The calf that was slain in this offering was bearing Aaron’s sin so that Aaron would no long be considered guilty. The sin-bearing calf absolved Aaron of his sin.

As we understand, this offering looked forward to the time when the perfect sin-bearing Son would bear away our sins at the cross once for all so that we would be reckoned righteous before a holy God. Apart from the sin-bearing Son we would still be in our sins and helpless and hopeless.

Praise be to God who gave his only, unique Son to be sin in our place, that in the ages to come he might have a people who delight in proclaiming his excellencies before all of creation.

Soli Deo Gloria!