Our Sages said: The seventy bulls the Jewish nation sacrificed in the Holy Temple during the holiday of Sukkot corresponds to the seventy nations, and the singular bull sacrificed on Shemini Atzeret corresponds to the one, unique nation – the People of Israel.
“This may be compared to a mortal king who said to his servants, ‘Prepare for me a great banquet’; but on the last day he said to his beloved friend, ‘Prepare for me a simple meal that I may derive benefit from you.’
The Midrash also explains:
‘This may be compared to the case of a king who made a banquet for seven days and invited all the people in the province during the seven days of the feast. When the seven days of the feast were over he said to his friend: ‘We have already done our duty to all the people of the province, let us now rejoice together, you and I, with whatever you can find – a pound of meat, fish, or vegetables.’ In a similar manner the Holy One, blessed be He, said to Israel: ‘On the eighth day you shall have a solemn assembly; let’s rejoice together with whatever you can find; with one bullock, one ram’(Bamidbar Rabbah 21:24).
Likewise, in the Zohar, it is also written that this day, Shemini Atzeret, is a day for the King himself – his day of joy together with Israel.
“This is analogous to a king who invited guests. The household people entertained them. At the end, the king said to his household, ‘Until now, I and you all entertained the guests. You offered sacrifices for the other nations every day, that is, the seventy bullocks. From now on, for one day, let me and you rejoice. This is the meaning of the verse ‘On the eighth day you shall have a solemn assembly’; “you” means offering sacrifices for yourselves” (Zohar 3, Emor 104:2).
“And when Israel heard this, they began to exalt God, saying: ‘This is the day that the Lord has made; let us rejoice and be glad in it’ (Psalms 118:24). Rabbi Avin said: ‘We do not know in which to rejoice: in the day, or in God? King Solomon came and interpreted: ‘We will exult and rejoice in you’ (Song of Songs 1:4) – ‘in you’, in your Torah, ‘in you’, in your salvation … “(Yalkut Shimoni Pinchas 782).
This is the special and unique meaning of Shemini Atzeret, which contains no distinctive mitzvoth, other than the mitzvah of rejoicing in God, His Torah, and His salvation.
Taken from Rabbi Eliezer Melamed’s book, “Peninei Halkha: Sukkot” and translated from Hebrew. All of Rabbi Melamed’s books can be found at: https://yhb.org.il/