I think the reason why God cannot be tempted is because there is nothing anyone could tempt him with. Jesus was tempted after fasting, which in effect simply means that he was offered something that he lacked.
If you were thirsty and someone offered you a drop of water on the tip of your tongue in exchange for the lives of all your grandchildren, I think you would agree that you were being tempted but that even with a sinful nature you would turn that offer down.
Your love for your grandchildren would make is utterly impossible to accept such a deal.
So if you who are evil are restrained by your nature then how much more would the Son of God be restrained?
In order to deny that Jesus was tempted, you have to deny Scripture: "For in that He Himself has suffered, being tempted, He is able to aid those who are tempted" (Heb. 2:18). And in the gospels, it clearly says that He was led into the wilderness "to be tempted." It matters not whether Satan offered Him two pepperoni pizzas or all the kingdoms of the world, the Word says that He was tempted. Had He given in to Satan in any way, sin would have entered the Godhead and God would have come undone. Jesus came in the flesh, and He had to endure all the discomforts, hunger, fatigue, uncomfortable heat, etc. Further, He did not go to the Cross because He could not have done otherwise. Jesus told Pilate, "Don't you know that I could call on my Father and He would send many legions of angels to Me? [paraphrased]." He sweated blood in the garden agonizing as to whether He should accept the torture and crucifixion that He knew was coming. He could have told the Father that He did not want to die for these Jews in Israel who hated Him. I would call this a temptation. Wouldn't you?
God gave us the freedom to choose, to sin or not sin, to love or hate Him. Yet, for some strange reason, we reason that God does not have freedom to choose. Why is that? Is God a robot? Is He a programmed computer? No. He is living, personal, relational, good, and loving. All these qualitative attributes require free choice (except that He is alive). It takes no faith for us to believe in a God who can't choose to be impersonal, not relational, bad, and unloving. If we have a God who can't break a promise, then his promise has no value.
I cherish my wife's love for me because she is free to love another. But she has freely chosen to love me. We can trust God not because He can't do otherwise, bu because He has a track-record of never, no not once, sinned, lied to us, broken His promise, denied us. Moral inconsistency is an absolute determinant for wrong. But we can find no moral inconsistency in God's relationship with us or His relationship within the Godhead. Jesus could go the grave knowing and trusting that God the Father would raise Him from the dead. This trust was not based on the fact that God the Father could not elect to leave Jesus in the grave. It was based on moral consistency within the Godhead over ions of time.
If God does not have free will, He could not have delegated free will to us. He can't give us what He has not got to give, nor can the effect be greater than the cause.
Jesus was tempted in all ways.