Solution
$$a : b = b : c$$
$$\frac{a}{b}\ =\ \frac{b}{c}$$
$$ac=b^2$$
$$b^2 = ac$$ Eq.(i)
Value of $$a^{6} : b^{6}$$ = $$a^{6} : (ac)^{3}$$ [Put Eq.(i) here.]
= $$a^{6} : a^{3}c^{3}$$
= $$a^{3} : c^{3}$$
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