One of the questions raised in the beginning of the maamar was: Why does the School of Shammai draw a comparison between the bulls offered on Sukkos and the Chanukah lights? The sacrifices offered on the Altar and the lights of the Menorah represented two different types of service.
On the basis of all the concepts explained above it is possible to understand the comparison between the Chanukah lights to Sukkos and the bulls offered on that holiday.וְעַל פִּי כָּל הַנַּ"ל יוּבַן הַפֶערְגְלַיְיךְ דְּנֵרוֹת חֲנֻכָּה לְסֻכּוֹת וּלְפָרֵי הֶחָג,
For Sukkos is characterized by the revelation of G‑d’s encompassing light.1 (This also applies to the bulls offered on that holiday.)כִּי עִנְיַן סֻכּוֹת (וְגַם עִנְיַן פָּרֵי הֶחָג) הוּא הִתְגַּלּוּת הַמַּקִּיפִים,
On Rosh HaShanah and Yom Kippur, the Divine service of the Jews evokes new light from G‑d’s essence. This light transcends the structure of the world and man’s internal powers. Hence, it is described as encompassing. This light is drawn down during the holiday of Sukkos and is
reflected in the actual sukkos in which Jews dwell, which encompass a person.בְּדֻגְמַת סֻכָּה כִּפְשׁוּטָהּ שֶׁמַּקֶּפֶת עַל הָאָדָם.
On the eighth day of Sukkos – Shemini Atzeres, a new dimension is added to the holiday. Sukkos as a whole is associated with the revelation of encompassing lights. On Shemini Atzeres,וּבַשְּׁמִינִי דְּסֻכּוֹת
those encompassing lights are drawn down and collected (the meaning of the term atzeres) in an internalized manner,נִמְשָׁכִים הַמַּקִּיפִים וְנֶעֱצָרִים גַּם בִּפְנִימִיּוּת,
similar to the manner in which the Divine service of the mesirus nefesh (of Chanukah) affects and permeates all the powers of the soul (as explained above, sec. 7).בְּדֻגְמַת הָעֲבוֹדָה דִּמְסִירוּת נֶפֶשׁ (דַּחֲנֻכָּה) שֶׁפּוֹעֶלֶת (כַּנַּ"ל) וְחוֹדֶרֶת בְּכָל כֹּחוֹת הַנֶּפֶשׁ.
On this basis, it can be understood why the two (festivals of Sukkos and Chanukah) are eight days. Above, it was explained that in general eight refers to a transcendent encompassing light. More particularly, however, it can be explained thatוְזֶהוּ מַה שֶּׁשְּׁנֵיהֶם (סֻכּוֹת וַחֲנֻכָּה) שְׁמוֹנָה יָמִים,
the number eight is a combination of one and seven.דְּמִסְפַּר שְׁמוֹנֶה הוּא א' ז',
Implied is that one (G‑d’s infinite light that transcends the Spiritual Cosmos)שֶׁהָא' (שֶׁלְּמַעְלָה מֵהִשְׁתַּלְשְׁלוּת)
is drawn down into the seven, (the structure of the Spiritual Cosmos),2 permeating it and elevating it,נִמְשָׁךְ בְּז' (הִשְׁתַּלְשְׁלוּת).
like the Chanukah lights that have a twofold effect on “the feet of the Tarmudites”:וּכְמוֹ שֶׁנֵּר חֲנֻכָּה פּוֹעֵל גַּם בְּרִגְלָא דְּתַרְמוֹדָאֵי בִּשְׁנֵי הָעִנְיָנִים,
Initially, they eliminate and nullify them.שֶׁבִּתְחִלָּה הוּא מְכַלֶּה וּמְבַטֵּל אוֹתָם
Afterwards, they bring about their transformation into holiness.וְאַחַר כָּךְ פּוֹעֵל בָּהֶם שֶׁגַּם הֵם יֵהָפְכוּ לִקְדֻשָּׁה,
Similar concepts apply with regard to the offering of the seventy bulls on Sukkos,עַל דֶּרֶךְ זֶה הוּא גַּם בְּהַקְרָבַת ע' פָּרֵי הֶחָג
which correspond to the seventy nations of the world.3שֶׁכְּנֶגֶד שִׁבְעִים אֻמּוֹת הָעוֹלָם,
Initially, the offering of these sacrifices causes the influence of these nations to progressively decrease, as the bulls offered decreased in number each day.שֶׁבִּתְחִלָּה פּוֹעֶלֶת הַהַקְרָבָה שֶׁהָאֻמּוֹת יִהְיוּ פּוֹחֲתִים וְהוֹלְכִים,
Afterwards, these offerings cause these nations to offer assistance to the Jewish people.וְאַחַר כָּךְ פּוֹעֶלֶת בָּהֶם שֶׁגַּם הֵם יְסַיְּעוּ לְיִשְׂרָאֵל,
As our Sages state,4 were the nations of the world to know how advantageous the Beis HaMikdash was to them, they would surround it with army camps5 to protect it.כְּמַאֲמַר רַזַ"ל אִלּוּ הָיוּ אֻמּוֹת הָעוֹלָם יוֹדְעִים מֶה הָיָה הַמִּקְדָּשׁ יָפֶה לָהֶם, קַסְטְרִיּוֹת הָיוּ מַקִּיפִים אוֹתוֹ כְּדֵי לְשָׁמְרוֹ כוּ'.
Bringing about the transformation of the nations of the worldדְּעַל יְדֵי שֶׁפּוֹעֲלִים בָּהֶם הָעִנְיָן דְּאִתְהַפְּכָא,
(also) causes, through the assistance these nations render, an increase in holiness,מִתּוֹסֵף עַל יָדָם סִיּוּעַ (גַּם) בַּקְּדֻשָּׁה,
in guarding the Beis HaMikdash,שְׁמִירַת הַמִּקְדָּשׁ.
which, as Rambam writes,6 contributes to the honor of the Beis HaMikdash:7 “A palace that is unguarded is not comparable to a palace that is guarded.”
This foreshadows the state of affairs in the Ultimate Futureוְעַל דֶּרֶךְ שֶׁיִּהְיֶה לֶעָתִיד לָבוֹא,
at which time, “I will transform the peoples… so that they all will call upon the name of G‑d and serve Him with one purpose.”8כַּאֲשֶׁר אָז "אֶהְפֹּךְ אֶל עַמִּים גוֹ' לְעָבְדוֹ שְׁכֶם אֶחָד",
Then, “Foreigners will stand and pasture your flocks.”9הִנֵּה אָז "וְעָמְדוּ זָרִים וְרָעוּ צֹאנְכֶם".
Similar concepts apply with regard to the offering of the seventy bulls, which correspond to the seventy nations:וְעַל דֶּרֶךְ הַקְרָבַת הָע' פָּרִים שֶׁכְּנֶגֶד ע' הָאֻמּוֹת,
Because of the offerings that relate to the nations of the world, there is added (on Shemini Atzeres) a sacrifice for the Jewish people in the Beis HaMikdash,10 i.e., an additional measure of holiness is contributed to the Divine service of the Jews themselves.וְעַד שֶׁעַל יְדֵי וּמִצַּד הָאֻמּוֹת נִתּוֹסֵף (בַּשְּׁמִינִי) קָרְבָּן לִבְנֵי יִשְׂרָאֵל בְּבֵית הַמִּקְדָּשׁ.

Summary

On the basis of the above explanations, it is possible to resolve one of the questions raised in the beginning of the maamar: Why is a comparison drawn between the bulls offered on Sukkos and the Chanukah lights despite the fact that they are two different types of service?
Sukkos is associated with the revelation of G‑d’s encompassing light. On Shemini Atzeres, that encompassing light is internalized. This parallels the manner in which the mesirus nefesh shown by the Jews at the time of the Chanukah struggle permeated their internal powers.
Just as the Chanukah lights have a twofold effect on undesirable influences, nullifying them and transforming them into good, the Sukkos offerings nullified the negative aspects of the nations of the world and transformed them into good. Moreover, as a result, there was an increase in holiness.