`omega` is an imaginary root of unity.
Prove that
If `a+b+c = 0` then prove that `(a + bomega + comega^(2))^(3)+(a+bomega^(2) + comega)^(3) = 27abc`.

Explanation

To prove that if \( a + b + c = 0 \), then

\[ (a + b\omega + c\omega^2)^3 + (a + b\omega^2 + c\omega)^3 = 27abc, \]

where \( \omega \) is a primitive cube root of unity, we can follow these steps:

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