Question abut the ambiguity of a maths problem.
Solution 1:
The true formula is that
$1^3+2^3+...+n^3=(1+2+...+n)^2$,
and you can prove this by induction. Assume that
$1^3+2^3+\cdots +(n-1)^3=(1+2+\cdots +(n-1))^2$,
then
$1^3+2^3+\cdots +n^3=(1+2+...+n-1)^2+n^3=\frac{n^2(n-1)^2}{4}+n^3=(1+2+\cdots n)^2.$