Let the roots be $a,$ $b,$ and $ab.$ Then by Vieta's formulas,
\[a + b + ab = -8,\]so $ab + a + b = -8.$ Completing the square in $a$ and $b,$ we get
\[(a + 1)(b + 1) = -7.\]The other root is then $-(a + b + 1) = ab.$ Hence,
\[c = -7 \cdot ab = \boxed{7}.\]
The equation $x^3 + 8x^2 - 4x + c = 0$ has three roots, one of which is the product of the other two. What is c?
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