It is given that $$\log_{6}a + \log_{6}b + \log_{6}c = 6$$, where $$a$$, $$b$$, and $$c$$ are positive integers that form an increasing geometric sequence and $$b - a$$ is the square of an integer. Find $$a + b + c$$.

(第二十届AIME2 2002 第3题)