Anisotropy of the cubic blue phase I of two types is observed in a cholesteric-nematic mixture using optical interference. The anisotropy of the first type is independent on the polarization of light. The second kind of anisotropy means dependence of the refractive index on the direction of polarizer in the plane perpendicular to the (110) direction in defect free BPI samples. The last effect depends on the ratio of the wavelength of measurements to the Bragg wavelength.