# Name for Product of Three Cubes

Is there a name for a number made out of three different cubics?

Editing Wikipedia, and wondered what word / term I should link to.

Ex: 74088 (everybody likes 42). $$42^3 = 2^3 \times 3^3 \times 7^3$$

• Do you require 3 prime factors, as in your example? Commented Sep 23, 2023 at 2:26
• Seems trivial. If $~n = a \times b \times c,~$ then ... Commented Sep 23, 2023 at 2:26
• @user2661923 Your description includes too many cubes. For example a=b=1, c=u is any cube at all, and a=6,b=5,c=7 is 210^3 , which is actually four cubes multiplied. Commented Sep 23, 2023 at 2:40
• Yes, the term is "cube". If a number is the product of 3 distinct cubes, then it itself is a cube. Nothing special about that Commented Sep 23, 2023 at 4:05
• "everybody likes 42" - if you mean the famous joke with $42$ , I neither find this joke good nor do I "like" $42$ (whaetever this even means). "three different cubics". You mean "product of three distinct cubes" ? I think this is already the perfect terminology , I am not aware of a further shortcut. Commented Sep 23, 2023 at 13:37

I suggest "cube of product of three distinct primes". Multiplication being both an associative and a commutative operation, we have for example $$2^3 \times 3^3 \times 7^3=(2 \times 3 \times 7)^3$$.

Since $$1$$ is not normally considered a prime, this formulation also avoids the issue raised in coffeemath's comment about the cube $$1$$ also being a factor of any cube.

• Hmm, I was actually hoping for something like a "Commutative cubic" or "Associative cubic" or similar, where it implies you can move the exponentiation inside or outside and it won't matter. That you can cube the terms, or cube their product, and its the same. Commented Sep 23, 2023 at 18:04