The order of the eighth day of inauguration:
And it was on the eighth day [of the inauguration], that Moshe called Ahron and his sons, as well as the elders of Israel and instructed them the offerings and order of the eighth day of inauguration.
When was the eighth day of the inauguration?
The inauguration began in the month of Adar. The eighth day of inauguration was on Rosh Chodesh Nissan. Rosh Chodesh Nissan merited to have the Mishkan established on its day and was crowned with ten crowns of glory. The Gematria of “On the eighth day Moshe called” is the same as “It was on the day of Rosh Chodesh Nissan”. However from the simple understanding of the verse, one can understand that the eighth day was on the 8th of Nissan.
What ten things occurred on Rosh Chodesh Nissan?
1. First day of Creation [as that year Rosh Chodesh fell on Sunday, and Sunday was the first day of creation].
2. First day that the Nessim brought their sacrifices.
3. Aaron and his sons began serving in the Mikdash as Kohanim.
4. First day that Karbanos were offered.
5. First day that the fire came down from heaven and consumed the sacrifices.
6. First day that the Kodshim were eaten.
7. First day that the Shechina resided on the Mishkan
8. First day that Birchas Kohanim was recited
9. First day that Bamos became forbidden.
10. First month of the year.
When did Ahron and his sons officially become Kohanim?
On the first of Nissan, the 8th day of inauguration.
Who offered the sacrifices on the 8th day?
Ahron and his children. Until then Moshe offered all the sacrifices. The offering of these sacrifices by the Kohanim inaugurated them into the Kehuna. The Karbanos that were offered by Ahron and his children served as atonement for the sin of the golden calf. The Chatas offering that was offered on this day was offered in a simalr manner to the offerings of Yom Kippur.
Why does the verse begin with the word “Vayehi/And it was” and not simply with the words “On the eighth day”?
The Talmud states that the term Vayehi is used to introduce tragic occurrences, and Nadav and Avihu died on this day of the Mishkan’s inauguration.
The Simcha on the eighth day:
The Simcha that Hashem had on the eighth day was as great as the joy Hashem had on the day of the worlds creation.
Why were the elders of Israel summoned?
The elders of Israel were summoned in order to witness that Ahron was chosen to be the Kohen Gadol by Hashem and not by Moshe. Alternatively, they were called in order to be present when the Karbanos of Klala Yisrael were offered.
 Toras Kohanim Shemini 1; Rashi ibid;
 Shabbos 87a; Rashi ibid
 Baal Haturim ibid
 Even Ezra ibid
 Shabbos 87a; Seder Olam 7
 Rashi ibid
 Shabbos ibid; Chizkuni ibid
 Ramban ibid
 Rashi ibid
 Chizkuni ibid