Per the Nicene Creed:
For our sake he was crucified under Pontius Pilate
Per the Holy Bible:
Pilate saw that he wasn’t getting anywhere and that a riot was developing. So he sent for a bowl of water and washed his hands before the crowd, saying, “I am innocent of this man’s blood. The responsibility is yours!”
And all the people yelled back, “We will take responsibility for his death—we and our children!”
So Pilate released Barabbas to them. He ordered Jesus flogged with a lead-tipped whip, then turned him over to the Roman soldiers to be crucified.
Some of the governor’s soldiers took Jesus into their headquarters and called out the entire regiment. They stripped him and put a scarlet robe on him. They wove thorn branches into a crown and put it on his head, and they placed a reed stick in his right hand as a scepter. Then they knelt before him in mockery and taunted, “Hail! King of the Jews!” And they spit on him and grabbed the stick and struck him on the head with it. When they were finally tired of mocking him, they took off the robe and put his own clothes on him again. Then they led him away to be crucified.
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Truth is...the "he was crucified" part isn't so much a matter of faith as the "for our sake" part. There is extra-biblical evidence that a man named Jesus was sentenced to death by crucifixion during Pilate's term as Roman governor. The amazing thing about that crucifixion is the belief that it was an example of the truly innocent willingly paying a penalty in the place of...for the sake of...the truly guilty.
Thank you, Jesus.