Prove by induction that for all $ninBbb N$.

Can anyone please show me how to solve this problem? I'm stuck
$$\sum_{k=1}^n k = \frac{n(n+1)}{2}$$
$$ and $$
$$\sum_{k=1}^n k^3 = \left(\sum_{k=1}^n k\right)^2$$

To prove by induction, it has to be as following:
1) Base Case: Show that P(n) is true.
2) Induction Hypothesis: Assume P(k) is true. for $k\in\Bbb N$
3) Induction Step: Show that P(k + $1$) is also true.