We have performed $^{11}$ B nuclear magnetic resonance (NMR) measurements to microscopically investigate an electronic structure of the ferromagnetic state in three different compositions of calcium-hexaboride single crystals. Although the crystal structure of Ca $B_{6}$ is cubic and three NMR lines may be expected for the nuclear spin 3/2 of $_{11}$ B, a larger number of NMR resonance peaks have been observed. The frequency and intensity of those peaks distinctively changes depending on the angle between crystalline axis and magnetic field. Analyzing this behavior, we find that the electric field gradient(EFG) tensor at the boron has its principal axis perpendicular to the six cubic faces with a quadrupole resonance frequency $v_{Q}$ 600 kHz. Even though the magnetization data highlight the ferromagnetic hysteresis, $^{11}$ B NMR linewidth data show no clear microscopic evidence of the ferromagnetic state in three different compositions of Ca $B_{6}$ single crystals.s.