# 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

- 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $1225$