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.
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.