So did Jesus claim to be the Son of God? Yes He did.
He forgave sins (Mark 2:5 - 12; Luke 5:20 - 25). He accepted worship (Matt 8:2; 14:33).
Remember when Jesus was with His disciples in Caesarea Philippi and He asked His disciples who people said He was? Some said John the Baptist, they said; some Elijah, others Jeremiah or one of the prophets. But who, said Jesus, do you say that I am? "And Simon Peter answered and said, 'You are the Christ, the Son of the living God.' Jesus answered and said to him, 'Blessed are you, Simon Bar-Jonah, for flesh and blood has not revealed this to you, but my Father who is in heaven'" (Matt 16:16, 17).
Remember when Jesus was talking with the unbelieving Jews about Abraham? Jesus told them "Most assuredly, I say to you, before Abraham was, I AM," using the name God used of Himself (Ex 3:14, 15). Some would dispute that Jesus was using God's name there, but the Jews understood what He meant all right. They took up stones to stone Him for what they saw as blasphemy. "But Jesus hid himself and went out of the temple, going through the midst of them, and so passed by" (John 8:58, 59).
Remember when Jesus was on trial before the Jewish authorities, how the high priest asked Him specifically "Are you the Christ, the Son of the Blessed"? He answered "I am. And you will see the Son of Man sitting at the right hand of the Power, and coming with the clouds of heaven" (Mark 14:61, 62).
Jesus is eternal (John 1:1). He was there at creation (John 1:3; Gen 1:1; Col 1:16). He is one with the Father (John 17:11). He is the giver of eternal life (John 10:28).
Not only His words, but His miracles spoke of who He was. The Old Testament law, for instance, gave detailed instructions in Leviticus 13 and 14 of what was to happen if a Jew was healed of leprosy. But from the completion of the law of Moses up to the coming of Christ there is no record of a Jew being healed of leprosy. The rabbis taught that only the Messiah would be able to heal a Jewish leper. So Jesus healed one and sent him to the priest (Luke 5:12 - 16).
The very basis of the Christian gospel is that man, being a sinner, was unable to save himself, so God came in the form of His Son, lived a perfect life and gave His life so that man's sin might be forgiven.
"And without controversy great is the mystery of godliness: God was manifested in the flesh, Justified in the Spirit, Seen by angels, Preached among the Gentiles, Believed on in the world, Received up in glory" (1 Tim 3:16).
"For God so loved the world that he gave his only begotten Son, that whoever believes in him should not perish but have everlasting life" (John 3:16).