בראשית כ"ה:י"ט
"וְאֵ֛לֶּה תּוֹלְדֹ֥ת יִצְחָ֖ק בֶּן־אַבְרָהָ֑ם אַבְרָהָ֖ם הוֹלִ֥יד אֶת־יִצְחָֽק"
When it says "ואלה" with a vav, it adds on to what it says previously whereas when it says "אלה" without a vav, it "disqualifies" what it says previously [שמות רבה ל, ב]. Indeed the Medrash [שם] says that "ואלה תולדות יצחק" adds on to what it says earlier "בני ישמעאל". What is the nature of this "addition" when one would think that the birth of Yitzchak would disqualify what it says earlier about the children of Yishmael??
Yitzchak was the first person circumcised at 8 days [עי' ב"ר ס,ה]. Since the slaves that are born in the house of a Jew are circumcised on the first day [: עי' שבת קל"ה ] - why do we only circumcise our own Jewish children at 8 days?
גמרא סנהדרין נ"ט - כדר' יוסי בר' חנינא דא"ר יוסי בר' חנינא כל מצוה שנאמרה לבני נח ונשנית בסיני לזה ולזה נאמרה. לבני נח ולא נשנית בסיני לישראל נאמרה ולא לבני נח.
" ... as Rabbi Yosei, son of Rabbi Ḥanina, says: Any mitzva that was first stated with regard to the descendants of Noach and was repeated at Sinai was stated for this group and for that group, i.e., it applies to both gentiles and Jews. But a mitzva that was stated with regard to the descendants of Noach and was not repeated at Sinai among the mitzvot given to the Jewish people was stated for the Jewish people and not for the descendants of Noach.
Milah was said to בני נח and repeated at Sinai "וביום השמיני ימול בשר ערלתו" and nevertheless בני נח are not commanded. Not only that but a בן נח with a Bris is called an ערל - uncircumcised while a Jew who doesn't have a Bris is called circumcised [נדרים ל"א, ב].
Why then are בני נח not commanded in Bris Milah?
The Gra writes as explained by his son Rav Avraham that the Bris includes all 613 mitzvos. ברי"ת is gematria 612 and it is the 613th so it encompasses all of the mitzvos. Bris Milah involves Mesirus Nefesh and Kiddush Hashem. The Zohar Hakadosh talks about how a person who is moser nefesh for mitzvos [even w/o actually dying] merits 400 worlds [which is alluded to in the 400 shekels that Avraham paid with for מערת המכפלה which was כסף meaning כיסופין - an expression of great "desire"]. Mesirus Nefesh catapults one to the highest worlds [עי' זוהר חיי שרה קכ"ג-קכ,ד]. Bris Milah is the highest expression in this world of Mesirus Nefesh [blood, knife, baby....] and thus merits one to reach the highest levels in the next world.
For the continuation - here.