L_{2}=\lim_{x\to 0}\frac{x-3\sin \frac{x}{3}}{x^{3}}=
\lim_{x\to 0}\frac{x-9\sin \frac{x}{9}+12\sin ^{3}\frac{x}{9}}{x^{3}}=
\lim_{x\to 0}\frac{x-9\sin \frac{x}{9}}{x^{3}}+12\lim_{x\to 0}\frac{\sin ^{3}\frac{x}{9}}{x^{3}}=
L_{3}+12\lim_{x\to 0}\left (\frac{\sin \frac{x}{9}}{\frac{x}{9}}  \right )^{3}\cdot \frac{1}{9^{3}}=
L_{3}+12\cdot 1^{3}\cdot \frac{1}{9^{3}}=L_{3}+\frac{4}{3^{5}}