$1-1^{3}+\left(\frac{-4}{-2}\right)^{3}$

Step 1 ：Given the mathematical expression \(1-1^{3}+\left(\frac{-4}{-2}\right)^{3}\)

Step 2 ：Following the order of operations (PEMDAS), we first simplify the expression inside the parentheses \(\frac{-4}{-2}\) which equals to 2

Step 3 ：Next, we raise this result to the power of 3, which gives us \(2^{3} = 8\)

Step 4 ：Subtracting 1 cubed (which is 1) from 1 gives us 0

Step 5 ：Finally, we add this result to 8, which gives us 8

Step 6 ：Final Answer: \(\boxed{8.0}\)