(i) Prove by induction or otherwise that for every $n \geqslant 1$,

$$\sum_{r=1}^{n} r^{3}=\left(\sum_{r=1}^{n} r\right)^{2}$$

(ii) Show that the sum of the first $n$ positive cubes is divisible by 4 if and only if $n \equiv 0$ or $3(\bmod 4)$.