  We derive an exact analytic expression for the high-temperature limit of the
Casimir interaction between two Drude spheres of arbitrary radii. Specifically,
we determine the Casimir free energy by using the scattering approach in the
plane-wave basis. Within a round-trip expansion, we are led to consider the
combinatorics of certain partitions of the round trips. The relation between
the Casimir free energy and the capacitance matrix of two spheres is discussed.
Previously known results for the special cases of a sphere-plane geometry as
well as two spheres of equal radii are recovered. An asymptotic expansion for
small distances between the two spheres is determined and analytical
expressions for the coefficients are given.
