Endoscopes are indispensable for minimally invasive optical applications in medicine and production engineering. The smallest lensless endoscopes often use digital optics to compensate the intrinsic distortions of light propagation of multimode or multicore fibers. However, due to the wavelength dependency of the distortion, the approach is restricted to a narrow spectral range, which prevents multispectral imaging modalities. We employ a spatial light modulator with a high stroke above 2π, to generate a hologram which minimizes overall phase distortion for multiple spectral bands. This enables lensless multicore fiber single-shot RGB endoscopy, for the first time in the world. Many applications in advanced manufacturing and biomedicine such as in vivo tissue classification are enabled.