Take both $n+195$ and $n-274$ $\mod{9}$

Let $n+195 = x^3$ and $n-274= y^3$ $\implies 469=x^3-y^3$ $\implies (x-y)(x^2+xy+y^2)=469=7.67$ Note that: $x-y < x^2+xy+y^2$ $\boxed {Case 1: x-y=1 ; x^2+xy+y^2=469}$ $\implies$ $x=13$ and $y=12$ $\implies$ $n=2002$ $\boxed {Case 2: x-y=7 ; x^2+xy+y^2=67}$ $\implies$ $x=9$ and $y=2$ $\implies$ There is no solution in n Thus $n=2002$