It is given in the question that,

a² + b² = - ab

a² + b² + ab = 0 (i)

We know that,

a³ – b³ = (a – b) (a² + b² + ab)

From (i), we have a² + b² + ab = 0

∴ a³ – b³ = (a – b) × 0

a³ – b³ = 0

Hence, option D is correct