I grow in a cupboard 2ft x 2ft x 6ft. I started off growing 4 plants. That did not work out too well. Then I reduced it to 2 and found that one plant always overgrew the other. Now I grow one plant at a time and find that I get more bud than from more overcrowded plants. A 1x1x3 grow is going to be difficult no matter which way you look at it. I suspect that heat will be the main problem. With only 3 cubic feet of space there is very little heat buffering and the grow will be subject to temperature swings that will stress the plants and reduce output. HID is right out! Way too much heat.

Even a substantial CFL is going to heat it up unless ventilation is very good. I think you are looking at LED for certain. Consider a Vipar B2x2. They are efficient and well up to what you want. One of these will fit in your box (just!). An alternative (and unorthodox solution) are Procyon 50W jobs. These are a bit expensive but are only the size of 2 coke cans, but use Cree chips and really punch out the light. The manufacturers claim they can handle 24"x24" so alowing for their exageration they may be ideal for your grow. Check them out at
http://www.homegrownlights.com/50wled.html
Best of luck!