Largest Number Not Expressible as Sum of Fewer than 8 Cubes

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Theorem

$8042$ is (probably) the largest positive integer that cannot be expressed as the sum of fewer than $8$ cubes.


Proof

It is believed that this entry is a mistake.

$8042 = 1^3 + 4^3 + 4^3 + 10^3 + 10^3 + 10^3 + 17^3$, among many other expressions.

However:

$8042$ is conjectured to be the largest positive integer that cannot be expressed as the sum of fewer than $\bf 7$ cubes.

$\bf {454}$ is proven to be the largest positive integer that cannot be expressed as the sum of fewer than $8$ cubes.


Historical Note

David Wells made this claim without providing a source in his Curious and Interesting Numbers of $1986$.

It has not been corroborated.


Sources