How would I replace this cube's reflection
With something like this?
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Try something like this for your World (Environment) Shader - it's just 2 Noise Textures with the detail turned down, scaled slightly differently and subtracted from each other. I also added ColorRamps to help "define" the shapes a bit better:
If you want the background to appear plain, while still providing lighting and reflections, mix your patterned background with a plain background using the Is Camera Ray output of a Light Path node as a mix factor. I also added another ColorRamp because the colors looked a bit blurred and indistinct on the reflections. I also ended up inverting the image (by way of the ColorRamp) because it looked a bit closer to your reference image, but I don't think it really matters that much.