I work in the borehole instrumentation industry, and lots of our customers get hyperspectral data from core. I'm working on a new data delivery and management platform, and I've made sure our data structures can handle hyperspectral images. Multidimensional arrays are front and centre. I too think of spectral images as "cubes".
One thing that stems from this is the question of how you visualise it. False colour mapping?
Photoshoplayers with color overlay or alpha shift towards the selected layer against a dark background ?
I found that people think that whatever you are doing must be extremely cool if you display it with the 3rd dimension being time. So create a video of each frame of the hyperspectral image and it shifts from one frame to another. Idk if it is super useful but if you put the video on a powerpoint it gets lots of excitement
Wikipedia has an article on hyperspectral imaging that also talks about how these images are acquired.