$W\left(x\right)=a{x}^3+b{x}^2+cx$  


$W\left(1\right)=a\cdot 1^3+b\cdot 1^2+c\cdot 1=a+b+c$

$W\left(1\right)+W\left(-1\right)=8$  

$a+b+c-a+b-c=8$  

$2b=8$  

$\underline{b=4}$