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 $a + b + c$.
Question:
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 $a + b + c$.
Answer:
Let's think step by step.

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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 $a + b + c$.
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