One of the most striking examples in the Gospels showing how the Lord Jesus spent time with the Father is the record of His spending a whole night in prayer. In Luke 6:12 we read, “And it came about in these days that He went out to the mountain to pray, and He spent the whole night in prayer to God.” The last phrase, “in prayer to God,” may be translated more literally, “in the prayer of God.” Although most versions of the Bible translate the phrase as an objective genitive – “in prayer to God,” it is equally proper to translate it as a subjective genitive – “in the prayer of God.” This simply means that in the prayer, God is not only the object to pray to, “to God,” but He is also the source of the prayer itself, “of God.”
Concerning the more literal translation of Luke 6:12, in his Commentary on the Gospel of Luke, Frederick L. Godet remarks, “The term proseuch touqeou, literally, prayer of God, is also a unique expression in the New Testament. It does not denote any special request, but a state of rapt contemplation of God’s presence, a prayer arising out of the most profound communion with Him.” Such a unique description of the Lord’s all-night vigil in prayer discloses something of what transpired during His prolonged and concentrated time with the Father. The prayer of God indicates that in and as a result of His “profound communion” with the Father, He merged with the burden and prayer of God; that is, He so allowed the Father to pass through Him during His communion and fellowship with Him that He became perfectly one with God. He merged with God. This meant God could pass through Him unhindered. He was emptied of self and completely open to the flow of prayer coming directly from God.
From "Spending Time With the Lord" by Bill Freeman