23 = 23 + 23 + 13 + 13 + 13 + 13 + 13 + 13 + 13

Only one other integer requires nine cubes of positive integers to represent its value as a sum of cubes. This other integer is between 200 and 300. Can you find it ?

$$239=5^3+3^3+3^3+3^3 +2^3+2^3+2^3+2^3+1^3$$

Well

$$\\5^3=125\\
so\\
257=5^3+5^3+1^3+1^3+1^3+1^3+1^3+1^3+1^3\\$$

Maybe there is a way to get 257 by adding less cubes   

Edited

Isn't that 257 ?

Sure looks like it.   Thanks anon :)