Computer Grow boxes are capable of cultivating mj. There are some problems, though. 1.) If you don't have a lowryder strain, you must do scrog/sog method. 2.) Even doing scrog/sog, I think it would take some time to get it right in that size of space. 3.) Yield will not be much in that size space.
That being said, I have seen some nice micro-grows in large computer grow-boxes (the server size uprights). As with any method, though, you must weight the pros and cons of each method against your personal situation. I don't think anyone here is going to tell you that this is the ideal method for individual consumption, but if circumstances require it...