If a = 500, b = 502 and c = 504, then the value of $a^3 + b^3 + c^3 - 3abc$

18072

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

If a = 500

b = 502

c = 504

Then the value of $a^3 + b^3 + c^3 - 3abc$ = \(\frac{1}{2}\) [(500 + 502 + 504) {( 500- 502)² + ( 502 - 504)² + (504 - 500)²}]

a³ + b³ + c³ - 3abc = \(\frac{1}{2}\) [(1506) {4+ 4 + 16}]

a³ + b³ + c³ - 3abc = 753 × 24 = 18072