Answer 1

ω is a complex cube root of unity
∴ ω³ = 1 and 1 + ω + ω² = 0
Also, 1 + ω² = - ω, 1 + ω = - ω²
and ω + ω² =  – 1
L.H.S. = (ω² + ω - 1)³
= (– 1 – 1)³
= (– 2)³
= – 8 = R.H.S.