The expression (a + b − c)3 + (a − b + c)3 − 8a3 is equal to:

Let a = b = c = 1

 (a + b – c)³ + (a – b + c)³ – 8a³ = 1 + 1 – 8 = (-6)

Checking option 3^rd.

6a(a – b + c) (c – a – b) = 6 × 1 × (-1) = (-6) Satisfied.

So the value of  (a + b – c)³ + (a – b + c)³ – 8a³ = 6a(a – b + c) (c – a – b)