Is $a^n b^n c^n$ context-free?
You are asking two different questions. First, is $\{a^nb^nc^n : n \geq 1 \}$ a context-free grammar? Second, is $\{a^nb^nc^n : n \geq 1 \}$ a context-free language?

The answer to the first question is No, since $\{a^nb^nc^n : n \geq 1 \}$ is not a grammar, let alone a context-free grammar; it is a language. What you probably meant to ask was: "Does $\{a^nb^nc^n : n \geq 1 \}$ have a context-free grammar?", which is the same as the second question.

The answer to the second question is also No. In fact, it is one of the standard examples of non-context-free languages, and as such most textbooks will have proofs to that effect.