Don't be sorry! Questions are good and this is what this forum is for.

On the inductive step in number 1, you should let $k\in\mathbb{N}$ and assume that

(1)
\begin{align} 1^3+2^3+\cdots+k^3=\left(\frac{k(k+1)}{2}\right)^2. \end{align}

Your goal is to prove that the formula works for $k+1$. That is, you must show that

(2)
\begin{align} 1^3+2^3+\cdots+k^3+(k+1)^3=\left(\frac{(k+1)(k+1+1)}{2}\right)^2. \end{align}

This isn't what you wrote above and this may be your problem. If not, I can provide another little hint.

To come up with a formula for number 2, try plugging in 1, 2, 3, etc. and see if you can find a pattern. For example, if $n=1$, then we get $\frac{1}{1\cdot 2}=\frac{1}{2}$. If $n=2$, then we get $\frac{1}{1\cdot 2}+\frac{1}{2\cdot 3}=\frac{2}{3}$. Do a few more and see if you see a pattern. What will the answer be for arbitrary $n$? (*Hint:* The formula is a single fraction involving $n$.)