I’m surprised I cannot find an image of the two devices side-by-side. Here is a mockup of the two in OpenSCAD using the dimensions from Wikipedia

dimensions_steam_machine = [156, 152, 162.4];  
dimensions_gamecube = [150, 161, 110];  

origin_steam_machine = [0, 0, 0];  
origin_gamecube = [dimensions_steam_machine[0] + 20, 0, 0];  

translate(origin_steam_machine) cube(dimensions_steam_machine, center=false);  
translate(origin_gamecube) cube(dimensions_gamecube, center=false);  

EDIT: Not sure exactly what is going on here. This is a Facebook post from November 2025 with what seems to be an empty shell of a Steam Machine. Perhaps it was a 3D printed mockup or something. Regardless, it seems to be enough to give a sense of the relative sizes of the devices.

https://www.facebook.com/eldozan1/photos/gamecube-vs-steam-machine-lo-que-me-impresiona-es-lo-pequeña-que-fue-la-gamecube/1383526843139907/

The Steam Machine is slightly bigger but it’s very close.

GameCube: 110 mm x 161 mm x 150 mm

Steam Machine: 152 mm x 162.4 mm x 156 mm