Evaluate using identities :

(i) 6³ – 9³ + 3³

(ii) 16³ – 6³ – 10³

(i) 6³ – 9³ + 3³

Here the identity used will be

a³ + b³ + c³ – 3abc = (a + b + c) (a² + b² + c² – ab – bc – ac)

∴ 6³ – 9³ + 3³

⇒ (6 + (– 9) + 3)(6² + (– 9)² + 3² – 6 × – 9 – (– 9)3 – 6 × 3) + 3 × 6 × – 9 × 3

⇒ 0 (36 + 81 + 9 + 54 + 27 – 18) – 486

⇒ – 486

(ii) 16³ – 6³ – 10³

Here the identity used will be

a³ + b³ + c³ – 3abc = (a + b + c) (a² + b² + c² – ab – bc – ac)

∴ 16³ – 6³ – 10³

= (16 – 6 – 10) (16² + (– 6)² + (– 10)² – 16 × – 6 – (– 6)(– 10) – (16)(– 10)) + 3(16) (– 6) (– 10)

= 0 (256 + 36 + 100 + 96 – 60 + 160) + 2880

= 2880