I was recently studying some Diophantine equations and the equation $x^2 - y^2 = z^3$ caught my eye.I knew that $x=(n+1)(n+2)/2$ , $y=n(n+1)/2$ , $z=(n+1)$ where $n \in \mathbb{N}$ gives a set of positive integer solutions.I wanted to obtain a different form of solution when suddenly the identity
$\{(m+t)^2 - (m-t)^2 \}(4mt)^2 = (4mt)^3$ came into my mind so I could produce $x=4mt(m+t)$ ,
$y=4mt|m-t|$ , $z=4mt$ where $m,t\in \mathbb{N}$ ; I would really like to know is this a (well) known solution? Is there any solution in other forms?