Sums of Consecutive Sequences of Squares that equal Squares

Theorem
The $24$th square pyramidal number is the only one which is square:
 * $1^2 + 2^2 + 3^2 + \cdots + 24^2 = 70^2$

while there are several Sum of Sequence of Squares which are square, for example:
 * $18^2 + 19^2 + \cdots + 28^2 = 77^2$

and:
 * $25^2 + 26^2 + \cdots + 624^2 = 9010^2$

Proof
We have:

and:

and: