Which of the following is considered cryptographically hard/easy?

Which of the following are easy, if any? Which are hard? and why.

Case 1) Given $x^3 \bmod N$, where $N$ is a composite number and we don't know any of the factors of $N$, find $x$.

Case 2) Given $x^3 \bmod p$, where $p$ is prime, find $x$.

Here is what I think but I don't fully understand it.

For case 1, this is assumed to be hard? In the RSA assumption, where $e = 3$, imagine $N$ being a large product of 2 primes. If we don't have any of the factors, can we say that this is hard? What other reasons can we say that this is hard? (or is this actually easy?)

For case 2, we assume to know all the factors of $p$, which apparently means this is cryptographically easy? We know that the number of elements (order) in $\mathbb{Z}_p^*$ is $p-1$. Does this mean that $3$ has an inverse $\bmod p - 1$? Using this fact, how can we recover $x$ given $x^3$?