You said, “We know he had his own will which differed from God's. Satan knew this when he tried to tempt Jesus into exercising his own will for selfish purposes. [Then you quoted, "For I have come down from heaven not to do my will but to do the will of him who sent me" John 6:38 & "Take this cup from me. Yet not what I will, but what you will” Mark 14:36.]”
But surely those verses prove that Jesus’ will was exactly the same as his Father’s will? Yes, he had his own will, but he chose to conform it utterly to the will of the Father. And who but he who had come from the bosom of the Father could know utterly the pefect and complete will of the Father? (See John 1:18.) The first verse you quoted shows that, before he came down from heaven to become the man, Jesus, he had decided to do what the Father willed. That included agreeing to be sent to earth to become flesh. He was not forced to become man, against his pre-human will! The second verse shows that right at the point before the crucifixion, his will remained resolutely the will of the Father. A third verse (Matthew 26:53-54) shows that the reason why he did not ask the Father to send twelve-plus legions of angels to deliver him at Gethsemane was that he knew such a request would stop the scriptures being fulfilled. He trusted in deliverance according to the will of the Father as in Psalm 119:170 – “Let my supplication come before thee: deliver me according to thy word.” And this, I suggest, is a recurring theme at every point where Jesus was tempted.
Still in Gethsemane, Jesus said, “I say unto you that this that is written must yet be accomplished in me” (Luke 22:37). A couple of hours or so earlier he had said, “And truly the Son of man goes as it was determined” (Luke 22:22). And, on the point of death on the cross, we are told, “Jesus knowing that all things were now accomplished, that the scripture might be fulfilled said, ‘I thirst’.” (John 19:28) Likewise, years earlier, when tempted by Satan, Jesus’ total command of, and belief in, the scriptures was key to him never sinning. The answer to your main question, ‘What is the biblical basis that Jesus could not sin?’ is that Jesus is the Word of God, and knew every word written in scripture to be the holy word of God which he spoke in order to resist temptation – because he agreed 100% with that written word. How could he not, given that he was the very Word of God incarnate (John 1:1-14)?
Jesus could only sin if there was any part of the holy scriptures he personally disagreed with. The Psalmist said, “Thy word I have hid in my heart, that I might not sin against thee” (Ps. 119:11). Jesus being the Greater David, David’s Lord, knew every jot and tittle of that written word, employing appropriate quotations from the scriptures to defeat Satan’s temptations, and any other temptation along the way to death on a cross. The eternal Son could say even more meaningfully than the writer of Psalm 119:89, “For ever, O Lord, thy word is settled in heaven.” It was settled there before any creation began and the Son, "who made everything that was made” had a settled will in total accord with the will of the Father
Consider also how Jesus is the Last Adam (Rom. 5:14-18; 1 Cor. 15:21-22 & 47). Satan cunningly deceived the first woman into thinking she could elevate herself to be as God with a special knowledge that God had warned against, and the first Adam chose to go along with that rather than risk losing what was precious to him. The Last Adam was tempted by Satan with an offer to short-circuit the cross – to obtain worldly glory and elevation there and then. Satan knew Jesus was physically weak and hoped to appeal to physical desires (for instant food, for instant heavenly deliverance, for instant glory and power) because he knew Jesus was now made lower than the angels. He tempted Jesus to use his divine powers for personal gratification. But Jesus rebuffed all three temptations with correct use of scripture. Sure, Satan knew he was dealing with the incarnate Son of God, but he could not resist the chance to at least try to trip him up while in a weakened state, just as he had ensnared the first Adam by getting him to make a personal, selfish choice that showed he did not believe God's word to him.
Finally, those who do not believe Christ to be the eternal Son of God but to have been created either as the first of God’s creations or only to have come into existence when conceived as the virgin Mary’s child, will think it perfectly possible that this creature could have sinned. Those who take a higher view of Christ as the uncreated Word of God disagree, and they have a deep biblical basis for so saying. I have only scratched the surface of this matter, but it all boils down to, “What think ye of Christ?” (Matthew 16:15 & 22:42)
You went on to ask what the biblical basis for him not being able to sin could be. Given that the Bible does not even ask that question, but does show us why Jesus did not sin, I would suggest that grasping the biblical information provided will cause those who believe it to ask different questions.