Solving a function for square numbers

Solving a function for square numbers

Essentially I'm curious; could a perfect square($x$ squared) be less than
the sum of all lesser perfect squares by a perfect square, and if so, what
would the smallest solution be. Take $36$ for example, $36 < 25+16+9+4+1$
by $19$, $19$ is not a perfect square.
$\dfrac{(x(x+1)(2x+1))}{6}$ sums the squares so I substitute $x-1$ and
take away the highest square and I get $\dfrac{(x(x-1)(2x-1))}{6}-x^2=$
"Perfect Square" how do find if there exists any integers $x$ that satisfy
such an equation?
Thank you!