What is the value of $a^3 + b^3 + c^3 - 3abc$, where a = 225, b = 226, and c = 227 ?

2034

What is the value of $a^3 + b^3 + c^3 - 3abc$,

where a = 225, b = 226, and c = 227

a³ + b³ + c³ - 3abc = \(\frac{1}{2}\)[(a + b + c) {( a- b)² + ( b - c)² + (c - a)²}]

a³ + b³ + c³ - 3abc = \(\frac{1}{2}\)  (225 + 226 +227) [(225-226)² +(226-227)² + (227-225)²]

= \(\frac{1}{2}\)  × 678 × (1 + 1 + 4)

= \(\frac{1}{2}\)  × 678 × 6

= 2034