Using the pumping theorem to show that this language is not context-free
Suppose that $L$ is context-free. Then the pumping lemma for context-free languages tells us that $L$ has a pumping length $p \ge 1$. We want to show that this leads to a contradiction, by exhibiting a string that is in $L$ but cannot be pumped in the manner specified in the lemma.

Consider the string $s = a^pb^pc^{(p^2)}$. Clearly, $s \in L$.

Now, see if you can show that all the possible ways of breaking down this string into the chunks specified in the lemma lead to a pumped string that is not in $L$.