Let the first term be \(a\) and the common ratio be \(r\).

The third term is given by \(ar^2 = -108\).

The sixth term is given by \(ar^5 = 32\).

Dividing the equations, \(\frac{ar^5}{ar^2} = \frac{32}{-108}\) gives \(r^3 = \frac{32}{-108} = \left( \frac{-8}{27} \right)\).

Thus, \(r = \left( \frac{-2}{3} \right)\).

For the first term, \(a = \frac{-108}{r^2} = \frac{-108}{\left( \frac{-2}{3} \right)^2} = -243\).

The sum to infinity is given by \(S_\infty = \frac{a}{1-r} = \frac{-243}{1 - \left( \frac{-2}{3} \right)} = \frac{-243}{\frac{5}{3}} = \frac{-729}{5} = -145.8\).