Is the King of Israel a Davidic Title?

In Psalm 89 verse 26, he meaning the Davidic king shall cry to me. This is one of a number of passage in Old Testament where we find that the king was seen as this son of God. And so this helps us kind of make sense of the progression in John 1. So maybe now we go to Zachariah and find out why Nathaniel would connect this kind of confusing thing that Jesus says about the fig tree with the king of Israel.