According to Catholic Encyclopedia (EC), the figure of the eighth day arises from certain traditions of the Old Testament.
For example, after a boy was born, “the eighth day was the day of circumcision.” Furthermore, “it was also the eighth day on which the festival of dedication of the Temple under Solomon and its purification under Hezekiah concluded,” the EC indicates.
At the origin of Christianity, no octave was celebrated. But the EC describes that in the 4th century the octaves of Easter and Pentecost emerged. Likewise, it indicates that “the first octave” known in Christianity was the celebration for the “Dedication of the churches of Tire and Jerusalem, under Constantine”, which lasted eight days with solemnities.