||In this paper we report a comprehensive study of the magnetic susceptibility (x), resistivity (p), and specific heat (C-P), down to 0.5 K of the cubic CeIn3-xSnx alloy. The ground state of this system evolves from antiferromagnetic (AF) in CeIn3 (T-N = 10.2 K) to intermediate-valent in CeSn3, and represents the first example of a Ce-lattice cubic non-Fermi liquid (NFL) system where T-N(x) can be traced down to T = 0 over more than a decade of temperature. Our results indicate that the disappearance of the AF state occurs near x(c) approximate to 0.7, although already at x approximate to 0.4 significant modifications of the magnetic ground state are observed. Between these concentrations, clear NFL signatures are observed, such as rho(T) approximate to rho(0) + A T-n (with n < 1.5) and C-P(T) proportional to -T ln(T) dependencies. Within the ordered phase a first order phase transition occurs for 0.25 < x < 0.5. With larger Sn doping, different weak rho(T) dependencies are observed at low temperatures between x = 1 and x = 3 while C-P/T shows only a weak temperature dependence.