Solutions to Approximate Fermat Equation x^3 = y^3 + z^3 Plus or Minus 1/Mistake

Source Work

 * The Dictionary
 * $729$
 * $729$

Mistake
Mistake $1$:
 * $9^3$ and the $2$nd smallest cube to be the sum of $3$ cubes: $9^3 = 1^3 + 6^3 + 8^3$. This makes $7^3$ the smallest solution to the approximate Fermat equation, $x^3 = y^3 + z^3 + 1$.

Mistake $2$:
 * The next such solution is $104^3 = 64^3 + 94^3 + 1$.

The first mistake is that it is not $7^3$ but $9^3$ which is the solution to that equation.

The second mistake is that $104^3 = 64^3 + 94^3 - 1$.