We report on a muon spin relaxation and rotation (mu SR) study in cubic Ca0.995La0.005B6. The oriented sample has practically the lattice parameters of CaB6 - space group Pm3m. A mu SR investigation of CeB6, isostructural with CaB6 and with nearly the same lattice constants, has shown that the implanted mu(+) are located at the crystallographic d site and are immobile up to at least 200 K. Surprisingly, this is different for the mu(+) in CaB6: they are at the interstitial 8 g site, and already for the lowest temperature range of the study, between 1. 8 and similar to 7 K, an apparently constant muon-spin relaxation of dynamical origin is present. This relaxation can only be explained by a mobile mu(+), e.g., by quantum diffusion, implying a hopping rate of - 2 x 105 s(-1). Between similar to 7 and similar to 70 K one observes an intermediate regime with slowly increasing mobility. True long range mu(+) diffusion appears to set in above similar to 70 K. This picture describes in a consistent way a comprehensive set of zero-field, longitudinal-field and transverse-field mu SR measurements performed for sample temperatures between 1.8 and 300 K. (c) 2005 Elsevier B.V. All rights reserved.