Defining Grammar for Given Language
Both of your languages are context-free and not regular. The first one can be generated using the following grammar:
$$
S \to a S \mid a S b \mid aab
$$
The second one can be generated using the following grammar:
$$
S \to aaSbbb \mid aabbb
$$

You can show that these languages are not regular using the pumping lemma or using Myhill–Nerode theory. Let me briefly indicate how to do so using the pumping lemma.

For the first language, suppose it were regular. Let $p$ be the constant promised by the pumping lemma. Then the word $a^{p+1} b^p$ is in your language. According to the lemma, it can be written as $xyz$, where $|xy| \leq p$ consists solely of $a$'s, and $y \neq \epsilon$. But then $xy^0z$ is not in your language.

The second language is even simpler, and left to you.