How can an understanding of Christ’s crucifixion keep us from thinking we need to earn God’s favor? BIB 536-4-1

This question can be answered with this one verse, “For God so loved the world, that he gave his only begotten Son, that whosoever believeth in him should not perish, but have everlasting life.” John 3:16 KJV
The crucifixion of Christ was prophesied in the Old Testament many times. That the crucifixion happened as prophesied substantiates the Bible as the inspirited Word of God. A few of the prophetic verses from the Old Testament that directly relate to us and that were fulfilled include:
Isaiah 53:5, “But he was wounded for our transgressions, he was bruised for our iniquities: the chastisement of our peace was upon him; and with his stripes we are healed.”
Isaiah 52:13-14, "See, my servant will prosper; he will be highly exalted. Many were amazed when they saw him - beaten and bloodied, so disfigured one would scarcely know he was a person."
Isaiah 53:4-6, "Yet it was our weaknesses he carried; it was our sorrows that weighed him down. And we thought his troubles were a punishment from God for his own sins! But he was wounded and crushed for our sins. He was beaten that we might have peace. He was whipped, and we were healed! All of us have strayed away like sheep. We have left God's paths to follow our own. Yet the Lord laid on him the guilt and sins of us all”
Isaiah 53:8, “From prison and trial they led him away to his death. But who among the people realized that he was dying for their sins - that he was suffering their punishment?"
Isaiah 53:10, “Yet it pleased the Lord to bruise him; he hath put him to grief: when thou shalt make his soul an offering for sin, he shall see his seed, he shall prolong his days, and the pleasure of the Lord shall prosper in his hand.”
In addition Psalm 22, could have been dictated from the cross.
God stepped out of eternity to become a man and suffer and die in our place. After two thousand years Jesus remains the most important man ever; He was, He is and He will forever be. I've heard it said that it wasn't the nails that held Jesus to the cross; it was His love for us. The crucifixion paid for our (my) sins so that we (I) can stand before God. Ephesians 2:8, “For by grace are ye saved through faith; and that not of yourselves: it is the gift of God:”

Added Later:

 I am so thankful that my sins are covered by the blood of Jesus.
Always the "Watchman on the Wall," I was sent a link to an article about Muslims crucifying other Muslims. To date I understand that this evil and barbaric behavior has been pretty much internal and I haven't read of any Christians being so horribly murdered. However, Muslim or Christian this is deplorable.
"Arab Spring run amok: 'Brotherhood' starts crucifixions: "The Arab Spring takeover of Egypt by the Muslim Brotherhood has run amok, with reports from several different media agencies that the radical Muslims have begun crucifying opponents of newly installed President Mohammed Morsi." http://www.wnd.com/2012/08/arab-spring-run-amok-brotherhood-starts-crucifixions/
Sura 5:33 of the Quran, " The just retribution for those who fight GOD and His messenger, and commit horrendous crimes, is to be killed, or crucified, or to have their hands and feet cut off on alternate sides, or to be banished from the land. This is to humiliate them in this life, then they suffer a far worse retribution in the Hereafter."