Factorize:

216 + 27b³ + 8c³ – 108bc

We know that,

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

Using this formula, we get

= (6)³ + (3b)³ + (2c)³ – 3 (6) (3b) (2c)

= (6 + 3b + 2c) [(6)² + (3b)² + (2c)² – (6) (3b) – (3b) (2c) – (2c) (6)]

= (6 + 3b + 2c) (36 + 9b² + 4c² – 18ab – 6bc – 12ac)