1. An image forming apparatus comprising: an image forming unit which forms an image on a sheet by using color materials of a plurality of colors on the basis of image data; a color conversion unit which converts a color space of the image data to a color space of the color materials used by the image forming unit by using a multi-dimensional LUT; a storage unit which stores a mixed-color pattern including a gradation of tones of a mixed color and a reference value of each of the tones, the mixed color made of at least two colors among the plurality of colors; and a control unit which forms an image of the mixed-color pattern on the sheet with the image forming unit, compares color values representing color shades for each of the tones between an observed value of the image of the mixed-color pattern formed on the sheet and the reference value of the mixed-color pattern stored in the storage unit, and determines that the multi-dimensional LUT needs to be updated and updates the multi-dimensional LUT if a difference of the color values is determined to be large on the basis of a threshold value.