We develop a deep learning network to estimate the illumination spectrum of hyperspectral images under various lighting conditions. To this end, a dataset, IllumNet, was created. Images were captured using a Specim IQ camera under various illumination conditions, both indoor and outdoor. Outdoor images were captured in sunny, overcast, and shady conditions and at different times of the day. For indoor images, halogen and LED light sources were used, as well as mixed light sources, mainly halogen or LED and fluorescent. The ResNet18 network was employed in this study, but with the 2D kernel changed to a 3D kernel to suit the spectral nature of the data. As well as fitting the actual illumination spectrum well, the predicted illumination spectrum should also be smooth, and this is achieved by the cubic smoothing spline error cost function. Experimental results indicate that the trained model can infer an accurate estimate of the illumination spectrum.