Cubing a simple thing I am trying to expand $\quad (x + 2)^3 $
I am actually not to sure what to do from here, the rules are confusing. To square something is simple, you just foil it. It is easy to memorize and execute. Here though I am not sure if I need to do it like multiplication where I take one $(x + 2)$ term and multiply by another or if I need to multiply all $(x + 2)$ terms by it. 
I want to treat it like how I would square it so I just square it and then I am left with the result and the $(x + 2)$ term. This is wrong and I do not know why. I get this
$$(x^2 + 4x + 4)(x + 2)$$
This is wrong and I am not sure why. So not I try the other way, multiplying everything by everything. This leaves me with
$$(x^2 + 4x + 4)(x^2 + 4x + 4)$$
Which is again wrong. I have exhausted all my options and nothing results in a correct answer and I am not sure why.

Your idea to do this:
$$(x^2 + 4x + 4)(x + 2)$$
was correct, because $(x + 2)^2 = (x^2 + 4x + 4)$. So it follows that $(x + 2)^3 = (x^2 + 4x + 4)(x + 2)$.
Let's try just multiplying it out:
To multiply $(x^2 + 4x + 4)$ by $(x+2)$, we'll multiply every term in $(x^2 + 4x + 4)$ by every term in $(x+2)$.
That's easy to do, and easy to visualise, because $(x^2 + 4x + 4)\cdot (x + 2)$ is the same as $(x \cdot(x^2 + 4x + 4)) + (2 \cdot (x^2 + 4x + 4)).$
$$(x \cdot(x^2 + 4x + 4)) = x^3 + 4x^2 + 4x$$
$$(2 \cdot (x^2 + 4x + 4)) = 2x^2 + 8x + 8$$
Add the two: 
$$x^3 + \color{red}{4x^2} + \color{blue}{4x} + \color{red}{2x^2} + \color{blue}{8x} + 8 = x^3 + 6x^2 + 12x + 8$$
