Question 147096
There are no vertical asymptotes, the denominator does not go to zero.
There are no horizontal asymptotes, as x goes to infinity, the function looks like y=x, as you can see from the graph below. 

{{{ graph( 300, 300, -100, 100, -100, 100, (x^3+8)/(x^2+4)
) }}}
The second graph shows the behavior of the graph near zero. 
{{{ graph( 300, 300, -5, 5, -10, 10, (x^3+8)/(x^2+4)
) }}}