Step 1 :\(\log _{6}\left(36 x^{3}\right) = \log _{6}(36) + \log _{6}(x^{3})\)
Step 2 :\(\log _{6}(36) + \log _{6}(x^{3}) = \log _{6}(36) + 3\log _{6}(x)\)
Step 3 :\(\log _{6}(36) + 3\log _{6}(x) = 2 + 3\log _{6}(x)\)
Step 4 :\(\boxed{2 + 3\log _{6}(x)}\)