St. Cyril on the Circumcision of Christ

Christ therefore ransomed from the curse of the law those who being subject to it, had been unable to keep its enactments. And in what way did He ransom them? By fulfilling it. And to put it in another way: in order that He might expiate the guilt of Adam's transgression, He showed Himself obedient and submissive in every respect to God the Father in our stead: for it is written, "That as through the disobedience of the One man, the many were made sinners, so also through the obedience of the One, the many shall be made just." He yielded therefore His neck to the law in company with us, because the plan of salvation so required: for it became Him to fulfil all righteousness. For having assumed the form of a slave, as being now enrolled by reason of His human nature among those subject to the yoke, He once even paid the half shekel to the collectors of the tribute, although by nature free, and as the Son not liable to pay the tax. When therefore them seest Him keeping the law, be not offended, nor place the free-born among the slaves, but reflect rather upon the profoundness of the plan of salvation.

On the eighth day, therefore, Christ is circumcised, and receives  His Name: for then, even then, were we saved by Him  and through Him, "in Whom, it saith, ye were circumcised with a circumcision not made with hands in the putting off of the fleshly body, with Christ's circumcision, having been buried together with Him in baptism, wherein also ye were raised with Him." His death, therefore, was for our sakes. as were also His resurrection and His circumcision. For He died, that we who have died together with Him in His dying unto sin, may no longer live unto sin: for which reason it is said, "If we have died together with Him, we shall also live together with Him." And He is said to have died unto sin, not because He had sinned, "for He did no sin, neither was guile found in His mouth," but because of our sin. Like as therefore we died together with Him when He died, so shall we also rise together with Him. ...
But after His circumcision, the rite was done away by the introduction of that which had been signified by it, even baptism: for which reason we are no longer circumcised.

COMMENTARY OF ST. CYRIL, PATRIARCH OF ALEXANDRIA, UPON THE GOSPEL OF ST. LUKE.(1859) BOOK I, PAGE 19-20

Doxology of the Feast of The Circumcision

                        Our Lord Jesus Christ,
The True Son of God,
Who was incarnate of the Virgin—
She brought Him forth as a Good One—

On the eighth day
Of His glorious birth,
Received unto Him the circumcision,
According to the custom of the Law.

Rejoice with us today,
All ye Christian nations,
For Christ has received unto Him
The circumcision on our behalf,

That He may set us free
From the bonds of the Law,
And grant unto us
His perfect gifts.