Is a^mb^n where m=n^2 a CFL?
This is not a context-free language, as an immediate consequence of Parikh's theorem.

In terms of pushdown automata, there is no way for a PDA to keep track of the number of $b$'s in the string in a way it can access repeatedly while reading (or popping) the $a$ part of the string. This is an essential feature of context-free languages; it is the same reason why languages such as $\{a^n b^n c^n d^n | n &gt; 0\}$ are not context-free.

For more examples, check out our reference question on proving languages are not context-free.