$(1^3+1)(2^3+1)\cdots(n^3+1)$ is not a cube
  For a positive integer $n,$ define $$C_n=\prod_{k=1}^n(k^3+1).$$ In this paper we prove that there are no cubes in the integer sequence $C_n,~n=1,2,\cdots.$ 
Chuan Ze Niu
math.NT