Factorize:

8 – 27b³ – 343c³ – 126bc

We know that,

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

Using this formula, we get

= (2)³ + (-3b)³ + (-7c)³ – 3 (2) (-3b) (-7c)

= (2 - 3b - 7c) [(2)² + (-3b)² + (-7c)² – (2) (-3b) – (-3b) (-7c) – (-7c) (2)]

= (2 - 3b - 7c) (4 + 9b² + 49c² + 6b – 21bc + 14c)