Knowing that $a b c=8$, with $a, b, c$ positive, what is the minimum value of $a+b+c$?
By the Arithmetic Mean-Geometric Mean Inequality (AM-GM Inequality): $\frac{a+b+c}{3} \geqslant \sqrt[3]{a b c}$.

Therefore, $a+b+c \geqslant 3 \cdot \sqrt[3]{8}=6$. This bound is indeed achieved with $a=b=c=2$.