Numbers whose Difference equals Difference between Cube and Seventh Power/Mistake

Source Work

 * The Dictionary
 * $125$
 * $125$

Mistake

 * $5^3 - 2^7 = 5 - 2$. The only known matching pattern is $13^3 - 3^7 = 13 - 3$.

In fact $5^3 - 2^7 = -3$, not $3$.