Square Numbers which are Sum of Sequence of Odd Cubes

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Theorem

The sequence of square numbers which can be expressed as the sum of a sequence of odd cubes from $1$ begins:

$1, 1225, \ldots$



Proof

We have that:

$1225 = 35^2 = \displaystyle \sum_{k \mathop = 1}^5 \paren {2 k - 1}^3 = 1^3 + 3^3 + 5^3 + 7^3 + 9^3$



Sources