The sum of cubes of first n numbers is given by: $\left [ \frac{n(n+1)}{2} \right ]^{2}$
Leading term: $n^{4}$
Hence, for big-Oh, anything equal or above $n^{4}$ is correct.
III is correct
The sum of the cubes isn't a variable value for a given input. $n^{4}$ is the lower bound, too. So $n^{4}$ or anything less than that works.
IV is correct
Both tight upper and lower bounds can be $n^{4}$ because again, the sum of the cubes isn't a variable value for a given input. So, the value would always be $\Theta (n^{4})$
I is correct, and II is incorrect.
Option C
Another method to solve this is replace
O by ≤
Ω by ≥
Θ by =
And compare with $n^{4}$