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1 And the LORD spake unto Moses, saying, 2 Speak unto the children of Israel, saying, If a woman have conceived seed, and born a man child: then she shall be unclean seven days; according to the days of the separation for her infirmity shall she be unclean. 3 And in the eighth day the flesh of his foreskin shall be circumcised. 4 And she shall then continue in the blood of her purifying three and thirty days; she shall touch no hallowed thing, nor come into the sanctuary, until the days of her purifying be fulfilled. 5 But if she bear a maid child, then she shall be unclean two weeks, as in her separation: and she shall continue in the blood of her purifying threescore and six days. 6 And when the days of her purifying are fulfilled, for a son, or for a daughter, she shall bring a lamb of the first year for a burnt offering, and a young pigeon, or a turtledove, for a sin offering, unto the door of the tabernacle of the congregation, unto the priest: 7 Who shall offer it before the LORD, and make an atonement for her; and she shall be cleansed from the issue of her blood. This is the law for her that hath born a male or a female. 8 And if she be not able to bring a lamb, then she shall bring two turtles, or two young pigeons; the one for the burnt offering, and the other for a sin offering: and the priest shall make an atonement for her, and she shall be clean.
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[AD 430] Augustine of Hippo on Leviticus 12:3
It was certainly not for nothing that the commandment was given for the child “to be circumcised on the eighth day”; it can only have been because the rock, the stone with which we are circumcised, was Christ. It was “with knives of rock” or stone that the people were circumcised;“now the rock was Christ.” So why on the eighth day? Because in seven-day weeks the first is the same as the eighth; once you’ve completed the seven days, you are back at the first. The seventh is finished, the Lord is buried; we are back at the first, the Lord is raised up. The Lord’s resurrection, you see, promised us an eternal day and consecrated for us the Lord’s day. It’s called the Lord’s because it properly belongs to the Lord, because on it the Lord rose again. The rock has been restored to us; let those be circumcised who wish to say, “For we are the circumcision.”

Source: SERMON 169.3
[AD 61] Luke on Leviticus 12:8
And when eight days were accomplished for the circumcising of the child, his name was called JESUS, which was so named of the angel before he was conceived in the womb. And when the days of her purification according to the law of Moses were accomplished, they brought him to Jerusalem, to present him to the Lord; (As it is written in the law of the Lord, Every male that openeth the womb shall be called holy to the Lord;) And to offer a sacrifice according to that which is said in the law of the Lord, A pair of turtledoves, or two young pigeons. [Leviticus 12:8]
[AD 735] Bede on Leviticus 12:8
The Lord commanded in the law that those who could were to offer a lamb for a son or a daughter, along with a turtledove or a pigeon. But one who did not have sufficient wealth to offer a lamb should offer two turtledoves or two young pigeons. Therefore the Lord, mindful in everything of our salvation, not only deigned for our sake to become a human being, though he was God, but also he deigned to become poor for us, though he was rich, so that by his poverty along with his humanity he might grant us to become sharers in his riches and his divinity.

Source: HOMILY XV. ON THE PURIFICATION OF BLESSED MARY