In his Mishneh Torah, the Rambam includes a drawing of the menorah with all 22 of its goblets upside down. Considering how precise he was, these upside-down goblets can’t be the result of an oversight. The Rambam must have believed they actually appeared that way in the Mishkan. Perhaps he had a tradition passed down to him generation after generation. Perhaps, he had a source in the teachings of our Talmudic Sages that has not come down to us.
Whatever the case may be: Why would the goblets have been upside down? Generally speaking, components of mitzvos must be right side up. For example, the kerashim – the heavy planks of wood that comprised the walls of the Mishkan – had to be erected precisely like they stood when they were still trees (Sukkah 45b), from which we learn that “for all mitzvos, one fulfills them only when [held] in the direction of their growth” (e.g., lulav, esrog, etc.).
So why were the goblets an exception?
They were an exception for the same reason that the Beis HaMikdash’s windows were narrow on the inside and wide on the outside (I Melachim 6:4) – even though most windows are narrow on the outside and wide on the inside. Because the menorah’s purpose was not to illuminate the Mikdash but to spiritually illuminate the world (Menachos 86b with Rashi).
A goblet’s purpose generally is to hold liquid, for which it needs to be upright. But according to the quasi-mystical Torah commentaries of Bachyei and Recanati, the menorah’s goblets primarily symbolized giving others to drink, quenching their thirst by pouring liquid into them (in line with the menorah’s general purpose of illuminating the world). On a spiritual level, it symbolized the emanation of Divine flow of blessing from higher spiritual levels to the lower world. And one can only drink from a goblet if it is (at least partially) facing downward.
Most mitzvos, performed as part of one’s personal service of Hashem, are designed to elevate us toward Hashem. But when we need to influence others, we must first pour out. And that’s why the menorah’s goblets faced downward.
(Based on teachings of the Lubavitcher Rebbe)