Find all the solutions of diophantine eq: $x^3-2xy^2+y^3-s^2=0$ Given $x,y,s$ are natural numbers:
$$x^3-2xy^2+y^3-s^2=0$$
I found the solutions using wolfram alpha
$$(x,y,s) = (1,2,1), (6,10,4), (4,8,8)$$
But how do I prove these are the only solutions? Any tips or reference to papers that study this diophantine equation would be much appreciated.

An infinite set of solutions is found when $y=2x$. In this case the equation $x^3 - 2xy^2 + y^3 = s^2$ reduces to: 
$$x^3 = s^2$$
So we can choose $x=a^2$ for any positive integer $a$, so then $a^6 = s^2$, so $s=a^3$. So the following combination works for any positive integer $a$: 
$$(x,y,s) = (a^2, 2a^2, a^3)$$  
