Thanks, Jon Lewis, for sharing more details.
Yes, I saw in the texture file field, that a “hdr/radiance” was used. I do not prefer such files, as the color rendition is kind of low. It is however for pure brightness values fairly good. Note it is a 8bit per channel only (not even close a 32bit/channel!), and the RGB values become multiplied at once with a fourth [E] channel, as well 8bit, hence the horrible colors and a very low tolerance for changes. RGBE 4*8bit/channel. Even the developer abandoned it—and that is nearly two decades ago. I have no idea why it stays so long in use (Well I know, as it is only 8bit, it is small, but one pays a lot of fidelity of the scene for it,) It might be OK as final delivery format, as JPEG is for the web, but in production it should be avoided.
Anyway, sorry for my critical comment on that format.
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The idea to get this aesthetic re-establsihed, is dependent on a mixture of parameters.
First set up a transparency value that matches close your target.
Then set a refraction value, watch for that “inner cube” that is established. Its size is dependent on the refraction value. I would start with 1.5
The absorption color should be set, and the distance of it accordingly to the size of the cubes. The cubes seams pretty small, so the 100cm are just useless here, start with 3cm. Note that the scaling of an object during import will not go through those parameters! They stay and become not scaled.
The roughness of the transparence is another parameter that needs attention.
The environment [sphere] will closely change the “light” inside of the cube. Start with a gradient and set up extreme colors—so you know what is going on. If the brightness works nice, set the colors back! In the attached scene, compare the cube one time on frame zero and then on frame three.
Finally, if the environment is creating the right “light” inside the cubes, the reflection needs to be set up in the material [strength], not longer possible to change in the environment [sphere].
Additionally check the Fresnel Reflectivity, a good starting point might be 14%.
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My idea was here not to provide a solution file. My intention is more to make you analysis the scene, “what causes what”, and get an idea of how to get it done. I moved [from my point of view] from the strongest influence to the lowest. But a back and fore is most of the time needed, as these things are interactive.
A little bit glow [very tiny] might help, a post workflow as well.
My best wishes
Images from frame 0 and 1, the axis are from the environment/sphere. It changes the appearance heavily, try frame 3! If all cubes were in the scene, the “inter-reflections” will do their own to the results, keep that in mind.