$27{{\left[ {{\left( \frac{15}{36}\times \frac{12}{18} \right)}^{3}}\div {{\left( \frac{5}{6} \right)}^{3}} \right]}^{2}}=27{{\left[ {{\left( \frac{3\times 5}{{{3}^{2}}\times 4}\times \frac{3\times 4}{2\times {{3}^{2}}} \right)}^{3}}\div \left( \frac{{{5}^{3}}}{{{\left( 2\times 3 \right)}^{3}}} \right) \right]}^{2}}-27{{\left[ {{\left( \frac{5}{{{3}^{2}}\times 2} \right)}^{3}}\div {{\left( \frac{5}{2\times 3} \right)}^{2}} \right]}^{2}}$

$\to 27{{\left[ {{\left( \frac{5}{{{3}^{2}}\times 2}\times \frac{2\times 3}{5} \right)}^{3}} \right]}^{2}}=27{{\left[ {{\left( \frac{1}{3} \right)}^{3}} \right]}^{2}}={{3}^{3}}\times {{\left( \frac{1}{3} \right)}^{6}}=\frac{{{3}^{3}}\times {{1}^{6}}}{{{3}^{6}}}=\frac{{{3}^{3}}}{{{3}^{6}}}=\frac{1}{{{3}^{3}}}=\frac{1}{27}$