Technically speaking, black is a shade, color is a hue. Any color, if dark enough, becomes black. So, if the question was, "What shade are your sunglasses?", black would be a correct answer.
Physicists speak of the color spectrum, based on frequency alone, but it's very different from the "color wheel" which is dependent on human eye receptors. The rainbow exemplifies the physicists' color spectrum. Notice that it tends towards black at BOTH ends? It's not because there is no light, it's because humans can't see the far infrared and the high ultraviolet light. The color wheel, on the other hand, is based on the human eye's sensitivity to red, green, and blue light, so that it requires a 3D graph to plot out all the colors of the "color wheel". Because the relative strengths of red, green, and blue can be represented as a phase, this is the part where the "wheel" comes in. That is to say, very unlike the physicists' color spectrum, the hues form a cyclical wheel. Black is not on it, but would be at the center of it, if the radius is taken to represent brightness. If the radius is 0, then it's black.
There are more than one way to represent the "color space" of human vision. Another would be to use red, green, blue as axes of a 3D color plot, in which case black would be at the origin (0,0,0), while all "pure hues" which are 100% unsaturated would lie only on the planes formed by the axes. All the other colors in the R, G, B space would have some saturation, meaning a mixture of a pure hue and white (or more correctly, a neutral).
In the vernacular, any and all colors, hues, shades is called "a color", because it's something, isn't it? Don't we have color charts that show all the colors, including black and white? But the best painters are critically aware of the distinction between hue, shade, and saturation, it's their lifeblood.