I performed some sound attenuation test about a year ago when I was building my sound proof enclosure for my Shapeoko, and I found that foam, on its own, really doesn’t do much for isolating the noise of the router. Heavy and dense materials, like MDF and ply, performed far better. And layering dense materials on either side of a strong vibration-absorbing material, such as Sorbathane or silicone, worked best.
Basically, mechanical isolation between the interior of the box and the exterior is the key to sound isolation. During my testing, I found that simply elevating my Shapeoko on four rubber feet reduced noise by 6.5dB. I theorized that building a box-within-a-box with vibration-absorbing material in between would effectively block all sound, but I should point out that I didn’t experiment with that at full scale.