Yes, but, Peter preached to believe on the name of Jesus (Matthew 16:16), that he is Christ, the Son of God, nothing of the cross, nothing of his death and resurrection until the Lord opened their understanding........but his death was to forgive their sins under the covenant (Hebrews 9:15) and his resurrection was to ascend until his coming to sit on the throne of David (Acts 2:30).
John and all the disciples preached only the name of Jesus (John 20:31). John 3:16 says nothing of the cross.
This is an interesting observation, of emphasis in the written word, ie the letters written by Paul and those by the other apostles and elders. But I would add these are just some of the letters, and mostly they were preaching and not writing.
So the letters reflect a small part of their ministry, but summarise all the different aspects in the body of Christ.
Now the emphasis is agreed by all will not be commented on, because they all agree it. And over centuries of theologians learning and considering the different aspects, they agree it is one united whole.
It takes time for the whole ambit of the word to form in ones heart and mind. Some sentences put an idea, which has layers of authority and structure which at first can appear different until after a time they all make a whole. Then it becomes clear they were speaking to an eternal truth, but emphasising different aspects to different fellowships who had differing issues.
What has staggard me is facing heretics on forums, my arguments can be written out be me, dismissed or the same arguments lifted from scripture, authoritative. I then saw why they were structured as they were, because a subtle emphasis is easily missed, or one difference highlighted as an issue, rather than a personality expression. Once you begin to see universal truths and specific application, then things can become clearer.
On the subject of the cross, the cross is the ultimate symbol of sacrificial love, so where love is mentioned, the cross can also be put. The word "agape" in greek is often used, which christians adopted as the symbol of Jesus, that appears not to have existed before Jesus as a definition. So John pictures Peter being asked to you agape me, do your agape me, do you philio me. (John 21:15-17)
What Jesus is, is the atoning sacrifice, the lamb, the blood, forgiveness for sins, salvation, redemption which are all found in all the scriptures. Scripture is very unusual, it rarely repeats a phrase, but says the same thing in many different ways, so you need to read it all and meditate on it, and it will begin to speak to your heart, not like a concordance, but to those who seek after God and His face. God bless you