Show that 97³ + 14³ is divisible by 111.

We know that,

a³ + b³ = (a + b)(a² + b² - ab)

∴ 97³ + 14³ = (97 + 14)[97² + 14² - 97 × 14]

= 111[9409 + 196 - 1358]

= 111 × 8247.

∴ 111 × 8247 is divisible by 111

Hence, proved that 97³ + 14³ is divisible by 111.