Q.Evaluate $\sum_{r=1}^{5} r^3 = 1^3 + 2^3 + 3^3 + 4^3 + 5^3$.

Use $\sum r^3 = \left(\frac{n(n+1)}{2}\right)^2$ with $n = 5$.

Apply $\displaystyle\sum_{r=1}^{n} r^3 = \left(\dfrac{n(n+1)}{2}\right)^2$ with $n = 5$:

Independent check (direct addition): $1 + 8 + 27 + 64 + 125$. Adding: $1 + 8 = 9$, $+27 = 36$, $+64 = 100$, $+125 = 225$ — matches. …

Computing $\dfrac{(n(n+1))^2}{2}$ (divide after squaring) instead of $\left(\dfrac{n(n+1)}{2}\right)^2$ (divide before squaring) — order matters: here the wrong or …