Factorization is an art (5)

Algebra Level 4

f(x)=4x36x2+4x1\large f(x)=4x^3-6x^2+4x-1

If f(2016)+f(2015)++f(2015)+f(2016)=f(y) f(-2016)+f(-2015)+\cdots+f(2015)+f(2016)=-f(y), find yy.

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