Find a positive integer N and a_{1}, a_{2}, \ldots, a_{N}, where a_{k}=1 or a_{k}=-1 for each k=1,2, \ldots, N, such that
a_{1} \cdot 1^{3}+a_{2} \cdot 2^{3}+a_{3} \cdot 3^{3}+\cdots+a_{N} \cdot N^{3}=20162016
or show that this is impossible.
Find a positive integer N and a_{1}, a_{2}, \ldots, a_{N}, where a_{k}=1 or a_{k}=-1 for each k=1,2, \ldots, N, such that
or show that this is impossible.