A serious challenge:
Can someone find 3 positive whole numbers that solve this equation?
The numbers must be whole!
$$E_n \colon y^2 = x \bigl(x^2 + (4n(n+3)-3)x + 32(n+3)\bigr) =: x(x^2 + Ax + B),$$
where in our case $n=4$. Then the curve is known to have rank $1$, and thus there is a solution in positive integers of "truly enormous size", see the article "An Unusual Cubic Representation Problem" by Andrew Bremner. It is given by $$ x = 4373612677928697257861252602371390152816537558161613618621437993378423467772036; $$
$$ y = 36875131794129999827197811565225474825492979968971970996283137471637224634055579; $$
$$ z = 154476802108746166441951315019919837485664325669565431700026634898253202035277999 $$ There are other solutions in positive integers, of course, but this is the smallest one.