The octave or "eighth day" of Easter is Divine Mercy Sunday. It is sometimes called "Low Sunday" since is the lower of the two Sundays in the Easter octave. As the eighth day of Easter, it carries a special meaning.
Saint Augustine wrote that this eighth day of Easter is a sign of new birth and faith as it was prefigured by Old Covenant Circumcision:
This is the octave day of your new birth. Today is fulfilled in you the sign of faith that was prefigured in the Old Testament by the circumcision of the flesh on the eighth day after birth. When the Lord rose from the dead, he put off the mortality of the flesh; his risen body was still the same body, but it was no longer subject to death. By his resurrection he consecrated Sunday, or the Lord’s day. Though the third after his passion, this day is the eighth after the Sabbath, and thus also the first day of the week.There is a lot to unpack in this Augustine quote. The connection between circumcision and resurrection is an interesting one. Augustine interprets both as a removal of the mortality of the flesh. Note that it is not a removal of the body. Rather, it is a transformation of the body - a glorification.
Does anyone know of any other related texts?
 Office of Readings for Divine Mercy Sunday.