This looks like a mordell like equation
X²=Y³-25056
How to solve it? The exact equation is
(36x)²=(6y)³-25056
Is there any website has records of the equation x²=y³+k
For k>25000
There are no integral points on this curve as established by SageMath. Here is a code to run
X=237225/196, Y= $\pm$ 115541397/2744