Sayyiduna Ibn Abbas (may Allah be pleased with them both) said: "The Messenger of Allah (peace and blessings be upon him) performed tawaf and did ramal (brisk walking) in the first three circuits, to show the polytheists that he (peace and blessings be upon him) and his Companions had strength, and he walked normally in the remaining four circuits."
Hadith Referenceالمعجم الكبير للطبراني / باب العين / 11086