I just found out that $$\sum _{i=0}^n\:i^2= \frac{n\left(n+1\right)\left(2n+1\right)}{6}$$ and $$\sum _{i=0}^n\:i^3 = \frac{n^2\left(n+1\right)^2}{4}$$ but I don't understand how did we get the expression $\frac{n\left(n+1\right)\left(2n+1\right)}{6}$ from this $\sum _{i=0}^n\:i^2$.
Can you help me with this. Thank you in advance.