calculus - $lim_{xto0}frac{sin x-x}{x^3}$ without de l'Hospital's Rule?

I know, how to calculate $$\lim_{x\to0}\frac{\cos x-1}{x^2}$$ without differential calculus. Calculating $$\lim_{x\to0}\frac{\sin x-x}{x^3}$$ using de l'Hospital's rule or Taylor expansion is also easy.

Is there a method to calculate the previous limit without de l'Hospital's rule or stronger tools?