Factorize:

27a³ – b³ + 8c³ + 18abc

We know that,

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

Using this formula, we get

= (3a)³ + (-b)³ + (2c)³ – 3 (3a) (-b) (2c)

= [3a + (-b) + 2c] [(3a)² + (-b)² + (2c)² – (3a) (-b) – (-b) (2c) – (2c) (3a)]

= (3a - b + 2c) (9a² + b² + 4c²+ 3ab + 2bc – 6ca)