Find all integral solutions of the equation $x^n+y^n+z^n=2016$ 
Find all integral solutions of equation
  $$x^n+y^n+z^n=2016,$$
  where $x,y,z,n -$ integers and $n\ge 2$

My work so far:
1) $n=2$ $$x^2+y^2+z^2=2016$$
I used wolframalpha n=2 and I received the answer to the problem (Number of integer solutions: 144)
2) $n=3$ 
I used wolframalpha n=3 and I not received the answer to the problem 
How to do without wolframalpha?

An approach that can sometimes help to find solutions to this type of equation is to consider the prime factors of the given integer.  In this case:
$$2016 = 2^5.3^2.7 = 2^5(2^6-1) = 2^5((2.2^5)-1)$$
Hence:
$$\mathbf{2016 = 4^5 + 4^5 + (-2)^5}$$
And also (finding a solution of $x^3+y^3+z^3=252$ by trial and error or from this list):
$$2016 = 2^3.252 = 2^3(7^3 - 3^3 - 4^3)$$
Hence:
$$\mathbf{2016 = 14^3 + (-6)^3 + (-8)^3}$$
