2 Samuel 8 - As God had said to David that because he was a man of war and shed blood, he was not the one to build the Temple, so you see in this chapter David's conquering of other nations and expanding his kingdom. But note, the land he possessed was part of what God had promised Abraham in His covenant with him. Israel was to possess land from Egypt to the Euphrates, note verse 3. David was preserved by the Lord wherever he went.
2 Samuel 9 - David had made a covenant with Jonathan to always treat Jonathan's family favorably. This chapter shows David's concern for one of Jonathan's sons, Mephibosheth, who was lame from a childhood injury. This man, who was married and had children of his own, would be permitted to eat at David's table. David treated the son as if he was the father. God treats us as if we were His Son, and in fact, we are children of God!
1 Chronicles 18 - As David conquered more cities he would always store away the treasures, especially gold, to be used by Solomon to build and beautify the Temple. David was a good organizer and delegated various people into key positions to make sure his kingdom ran orderly.