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