FACTORIAL-CUBES !

Algebra Level 3

If X = 2014! , Y = 2015! , Z = 1/2015! find the value of

\(\frac { { \left( x+y+z \right) }^{ 3 }-{ \left( x+y-z \right) }^{ 3 }-{ \left( y+z-x \right) }^{ 3 }-{ \left( z+x-y \right) }^{ 3 }-23xyz }{ 2013! } \)

HINT : Assume a + b = 2y , b + c = 2z , c + a = 2x and a+b+c = x+y+z.

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