$a^*b^*c^* \setminus \{a^n b^n c^n | n ≥ 0\}$ is not regular using pumping lemma? $L=a^*b^*c^* \setminus \{a^n b^n c^n \mid n \geq 0\}$ can be proved as context-free by partitioning it as $L = \{a^nb^mc^* \mid n \neq m\} \cup \{a^*b^nc^m \mid n \neq m\}$ and further dividing each $\neq$ into smaller and larger. You will have four sets. You can give CFG's for each. Then since CFGs are closed under union, you have your proof.

Now how can I go around proving that $L$ is not regular? If you prove that the each of these four sets are not regular, you still can not prove that the union is not regular, can you?
Lets assume towards contradiction that L is regular.
Then, by closure properties, we have $\bar L$ is regular, and thus also $\bar L \bigcap (a^*b^*c^*)$ is regular. But calculating it, we find out $\bar L \bigcap (a^*b^*c^*)=\{a^nb^nc^n\}$ is not regular.