If a + b + c = 8, then the value of (a – 4)3 + (b – 3)3 + (c – 1)3 – 3 (a – 4) (b – 3) (c – 1) is

We have p³ + q³ + r³ – 3pqr = (p + q + r) (p² + q² + r² –pq – qr - rp)
Here p = a – 4, q = b – 3, r = c –1
So, given expression is (p + q + r) (p² + q² + r² – pq – qr – rp)
= (a – 4 + b – 3 + c – 1) (p² + q² + r² – pq – qr – rp)
= (a + b + c – 8) (p² + q² + r² – pq – qr – rp)
= (8 – 8) (p² + q² + r² – pq – qr – rp)
∴ (a – 4)³ + (b – 3)³ + (c – 1)³ – 3 (a – 4) (b – 3) (c – 1) = 0