For two constants $a$ and $b$ with $a < b$, define the function $f ( x )$ as
$$f ( x ) = ( x - a ) ( x - b ) ^ { 2 }$$
For the inverse function $g ^ { - 1 } ( x )$ of the function $g ( x ) = x ^ { 3 } + x + 1$, the composite function $h ( x ) = \left( f \circ g ^ { - 1 } \right) ( x )$ satisfies the following conditions. Find the value of $f ( 8 )$. [4 points]\\
(가) The function $( x - 1 ) | h ( x ) |$ is differentiable on the set of all real numbers.\\
(나) $h ^ { \prime } ( 3 ) = 2$