Find the partial fraction decomposition. \[ \frac{8}{x^{3}+4 x^{2}+4 x} \]

Step 1 ：The given expression is a proper rational function. To find the partial fraction decomposition, we first need to factorize the denominator. The denominator is a cubic polynomial and can be factorized by grouping.

Step 2 ：After factorizing, we can write the given expression as a sum of simpler fractions where the denominator of each fraction is a factor of the original denominator. We can then solve for the coefficients of these simpler fractions.

Step 3 ：The partial fraction decomposition of the given expression is \(-\frac{2}{x + 2} - \frac{4}{(x + 2)^2} + \frac{2}{x}\).

Step 4 ：\(\boxed{-\frac{2}{x + 2} - \frac{4}{(x + 2)^2} + \frac{2}{x}}\)