Largest Number Not Expressible as Sum of Fewer than 8 Cubes/Mistake

Source Work

 * The Dictionary
 * $8191$
 * $8191$

Mistake

 * This is probably the largest integer that cannot be represented as the sum of fewer than $8$ cubes.

Correction

 * $(1) \quad$ This should probably read:


 * This is probably the largest integer that cannot be represented as the sum of fewer than $7$ cubes


 * as we have:


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


 * $(2) \quad$ Also note that:
 * $8042 = 1340^3 + 1338^3 + \paren {-1339}^3 + \paren {-1339}^3 + 2^3$


 * so what it really ought to say is:


 * This is probably the largest integer that cannot be represented as the sum of fewer than $7$ positive cubes.

This entry has been corrected in of $1997$, so perhaps it was not even true in the first place.