HERE are two kings considered here: Solomon... and Jesus. Some of David's words apply to both of them and some of his words obviously are only about one. Let's focus on the greater of the two.
Jesus is certainly known as the Son, and He will be known as the King. He is the righteous Judge. He is delivering the poor. He is to be feared forever. He causes righteousness and peace to flourish. Absolute dominion is rightfully His and will be His full possession in time. He is a deliverer of the needy and of the helpless. He is the saver and redeemer of souls. Life, prayer and praise are His. His name will endure forever and all who are blessed, are blessed through Him. He is the wondrous expression of the Father and someday the whole earth will be filled with His glory. These are the claims of Psalm 72.
Psalm 72:6, 9 & 16 stand out in this song like they were printed in neon colors. "He shall come down like rain on the mown grass..." bringing revitalizing life and growth to all who have been cut down to size. All men will "bow before Him; and His enemies shall lick the dust" Hallelujah! And then, verse 16 speaks mysteriously about the way things will be during the millennial kingdom when the curse has been removed from the face of this old globe (Jeremiah 30:9 and Revelation 5:9 & 10). It points to the new agriculture of the kingdom. Normally, planting a handful of grain on top of a mountain is not likely to fill anyone's barns. But, when the living Word of God reigns on earth, Eden will return. Even the tops of mountains will be fruitful like nothing we have ever seen. Oh, how marvelous life will be (John 1:18). Even so pray to Him now... "Thy kingdom come!"