“In burnt offerings and sacrifices for sin You had no pleasure. Then I said, ‘Behold, I have come— In the volume of the book it is written of Me— To do Your will, O God'” (Hebrews 10:6-7).
The Gospel of John records several instances where Jesus signaled His intent to fulfill God’s will in accord with this passage…
“Jesus said to them, ‘My food is to do the will of Him who sent Me, and to finish His work'” (John 4:34).
“I can of Myself do nothing. As I hear, I judge; and My judgment is righteous, because I do not seek My own will but the will of the Father who sent Me” (John 5:30).
“For I have come down from heaven, not to do My own will, but the will of Him who sent Me” (John 6:38).
However, Luke’s Gospel may contain the greatest expression of that commitment…
“So [Jesus] came to Nazareth, where He had been brought up. And as His custom was, He went into the synagogue on the Sabbath day, and stood up to read.
And He was handed the book of the prophet Isaiah. And when He had opened the book, He found the place where it was written: ‘The Spirit of the Lord is upon Me, Because He has anointed Me To preach the gospel to the poor; He has sent Me to heal the brokenhearted, To proclaim liberty to the captives And recovery of sight to the blind, To set at liberty those who are oppressed; To proclaim the acceptable year of the Lord.’
Then He closed the book, and gave it back to the attendant and sat down. And the eyes of all who were in the synagogue were fixed on Him. And He began to say to them, ‘Today this Scripture is fulfilled in your hearing'” (Luke 4:16-21).
In referencing this Old Testament quote from our passage from Hebrews, one source observes, “The OT prophets had warned the Israelites that sacrifices alone would not please God. He desired obedience as well (Ps. 51:16, 17; Is. 1:13–17; Mark 12:33). This messianic psalm indicates that Jesus’ obedience to God the Father was one of the reasons His sacrifice was better than the OT sacrifices.” (1)
Another commentator adds…
“God’s will was a new covenant with all humanity established by Jesus’ death and resurrection (cf. Mark 10:45; 2 Cor. 5:21; Heb. 10:9). When animals died in sacrificial offerings they had no choice. Jesus willingly laid down His own life (cf. John 10:17-18).” (2)
(1) Radmacher, E. D., Allen, R. B., & House, H. W. (1999). Nelson’s new illustrated Bible commentary (p. 1650). Nashville: T. Nelson Publishers.
(2) Dr. Bob Utley, Hebrews 10 [10:7] Copyright © 2014 Bible Lessons International http://www.freebiblecommentary.org/new_testament_studies/VOL10/VOL10_10.html