summation - Prove a lower bound for $sum_{i=1}^n i^2$

Prove that

$$\sum_{i=1}^n i^2 \geq \frac{n^3}{3}$$ for all $n \geq 1.$

What I know: I know the basic format of how to make a proof with the basis and inductive step but I am unsure of how to prove this particular statement and expand it. This is for a data structures class by the way.
My attempt so far has been $1^2 + 2^2 +\cdots+n^2$ is $i^2$ expanded. Can anyone provide some insight or link me to similar examples on how to go about structuring this?

Thanks so much in advance I am really lost and haven't taken a proofs class before so it's all new to me.