Chapter 11.P, Problem 25P

Let $u=1+\frac{x^3}{3!}+\frac{x^6}{6!}+\frac{x^9}{9!}+\mathrm{...}$

$v=x+\frac{x^4}{4!}+\frac{x^7}{7!}+\frac{x^{10}}{10!}+\mathrm{...}$

$w=\frac{x^2}{2!}+\frac{x^5}{5!}+\frac{x^8}{8!}+\mathrm{...}$

Show that $u^3+v^3+w^3-3uvw=1$.