Is there a deeper significance of squares and cubes?

Question

I've noticed that many of the structures in the Mishkan as well as elsewhere in Judaism are cubes and squares, or multiples of cubes and squares.

• The luchot are two half-cubes which combine to make a full cube (1x1 ama)

• The Gold Mizbeach is 2x1 ama (or two 1 ama cubes [5tefach/ama]) with four cube corners

• The Copper Mizbeach is 5x10 amot (or two 5 ama cubes*) with 5x5 tefach cubes on its' four corners. *The actual measurements are a mix of 5 and six tefach amas, which changes it's actual size (Eruvin 4a & Menachos 98a), but it's rough description is 5x10 amot, 250 times the size of the luchot & 216 times the size of the Gold Mizbeach, and a quarter of the size of the Kodesh Kedashim.

• The Kodesh-Kedashim is a 10x10 ama cube

• The Holies is 20 ama x 10 ama (or two 10 ama cubes)

• The courtyard is 100x50 ama (or two 50 ama squared)

• Tefilin are 2 individual cubes.

• Tzizit have four-squares on their corners.

• The Shulchan is 6x12x9 ama (or 648 tefachim cubed, which is three times the volume luchot)

• The Lechem Panim were 5x10 tefachim and folded into 5x5 tefach squares.

• The choshen was 1x1 ama squared

• There were 50 letters on the Choshen's stones, 25 on each shoulder stone.

• The Parochet was 10x10 ama squared

Was it just an easy shape or ratio to make?

Edit: I've been thinking it has to do with the "pattern" that Hashem instructs Moshe to build the mishkan after, which He showed Moshe on Har sinai.

"According to all that I show you, the pattern of the Mishkan and the pattern of all its vessels; and so shall you do." (Terumah 25:9)

"And you shall erect the Mishkan according to its proper manner, as you will have been shown on the mountain." (Terumah 26:30)

Answer 1

R. Shalom Dovber Schneersohn (the fifth Lubavitcher Rebbe), in one of his discourses (Sukkos 5674, part of the series known as Beshaah Shehikdimu 5672, which he began delivering on Shavuos 100 years ago) gives an explanation that may bear on this.

He points out (in sec. 205) that there are two letters of the alef-beis that are completely sealed closed: final mem (which is square) and samech (which is round). The Zohar notes that the difference is that a square is something that "sits" in place without rolling around; it thus represents a level of Divinity that, even though it is "sealed" and beyond our ken, relates to our world and "enclothes" it. A circle (and the letter samech), by contrast, symbolizes an aspect of Hashem's energy that is beyond even the "chain of [spiritual] evolution" (seder hishtalshelus) that results in the various creations, physical and spiritual.

He also cites Emek Hamelech, that the underlying reason for this difference is that a square, with its four sides, is related to the four-lettered Name of Hashem (which in both form and meaning represents His creative energy).

Based on all of this, we might speculate that the squares and cubes in the Mishkan/Beis Hamikdash, and more generally in halachah, are meant to evoke this idea: they represent, and help us draw down into our world, that "enclothing" level of Divinity that is sourced in Hashem's Name.

Answer 2

There is a lot to unpack here kabbalistically but to give a very basic answer to your question repetition mathematically, linguistically or conceptually is a sign of emphasis in Judaism. In kabbalah you have the concept of magic squares (also referenced in the comments) as well as permutations of combinations of letters. Squares are used as a phyiscal manifestation of this spiritual concept.

The gemarah in nedarim (3:2) also states that squares are do not occur in nature.

Answer 3

For those looking for a more natural explanation. Squares are seen as supernatural, they rarely exist in nature without human creation. Squares, and things made into squares are a sign of our human status above nature, and our connection to the Divine.