Calculate $2^{(2^3)} - \left(2^2\right)^3$.
This problem involves exponents and parentheses, so I need to remember the order of operations and the rules of exponents. I know that parentheses come first, so I need to evaluate what is inside the parentheses before applying the exponents. Inside the parentheses, I have $2^3$ and $2^2$, which are both easy to calculate. I know that $2^3 = 8$ and $2^2 = 4$, so I can replace them in the expression. Now I have $2^8 - 4^3$. Next, I need to apply the exponents. I know that $2^8 = 256$ and $4^3 = 64$, so I can replace them in the expression. Now I have $256 - 64$. Finally, I need to perform the subtraction. I know that $256 - 64 = 192$, so that is the final answer.

