<s>[INST] Can i factor this expression: $x^3+y^3+z^3$ I have the following numerical expression, which is exactly equal to $1$

Text version:
(-(7 2^(2/3))/38 + 3^(2/3)/19 + (23 5^(2/3))/95 + (5 6^(1/3))/19 + 3/38 (5^(1/3) 6^(2/3)) - 10^(1/3)/19 - 3/190 (3^(1/3) 10^(2/3)) - (4 15^(1/3))/19 - 6/95 (2^(1/3) 15^(2/3)))*(2^1/3+3^1/3+5^1/3)

Image version:

according to this fact, $x^3+y^3+z^3$ would  be factorized at all and first factor of it should be $x+y+z$ if we set
$
x^3=2,y^3=3,z^3=5
$


If so then how to factor $x^3+y^3+z^3$ ?


PS. I tried to divide $x^3+y^3+z^3$ by $x+y+z$ and failed (got remainder).
 [/INST] You have the identity:
$$x^3+y^3+z^3-3xyz=(x+y+z)(x^2+y^2+z^2-xy-yz-xz)$$
As far as I know, this is the best you can do, though I'd be happy if someone proves me wrong.
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