AMC 12 2004b Problem 17

For some real numbers $a$ and $b$, the equation $$8x^3 + 4ax^2 + 2bx + a = 0$$ has three distinct positive roots. If the sum of the base-$2$ logarithms of the roots is $5$, what is the value of $a$?

$\mathrm{(A)}\ -256 \mathrm{(B)}\ -64 \mathrm{(C)}\ -8 \mathrm{(D)}\ 64 \mathrm{(E)}\ 256$