I was wondering if it was possible to record my guitar using only the following equipment:

Roland Micro Cube Amp which has a Rec Out socket at the back
Aux cable (1/8inch plug to 1/8inch plug)
Adaptor (1/8inch socket to 1/4inch plug)
Guitar lead (1/4inch plug to 1/4inch plug)
Microphone or headphone ports on Laptop (both of them 1/8inch sockets)
Cubase, Soundforge or any other computer programme i can record with.

If it's possible, then how do I actually set it up in e.g. Cubase, so that I can record and play back guitar? I've tried googling and youtubing this and I get nowhere.
It's definitely possible. The quality won't be as good as using a good interface though. I haven't used Cubase since...4 maybe? And only then briefly. Never used Soundforge but I've used ACID extensively and I would think the set up is about the same. Should go something like this:

After you've used the adapter to plug your guitar into your line in, check the "preferences" tab in your DAW. Under preferences, there should be something that says "recording" or "devices".. Go to that and make sure the device used for recording is Realtek Audio Driver (or whatever your system's default driver is). The output, by default, should be whatever audio driver your system uses. A lot of DAWs have other options for input like Wave Driver, etc.. So you may have to click around a bit to find what you're looking for. Open a track and hit the arm button. Once you start seeing a signal from your playing, you know you've found the right input source. After that, just hit record and go.
I'm guessing you would need a line-in on your pc. That way you could record everything directly out of the amp. Whether it's a laptop or a pc, there should be a line input, check it out.
What's a line input exactly?

Thanks, GenericGenocide, I can now record (using the standard mic 1/8inch socket). But I'm using Audacity (not sure if Acid would make the quality better?) My god the quality is awful lol. Noise level is unbearable. I guess it will do though for rough drafts until I get an interface
I've got a problem now. As soon as I start playing on the recording, the sound is full and has bass. After a few seconds of strumming, the soundwaves get smaller, like the volume is being reduced to compensate for too much noise or something? Then the sound becomes tinny with little bass. When I mute my strings and play again after a few seconds, it goes back to the full sound but then the same thing happens again. Any idea how to tackle that?
A line input is just the "line in" on your computer. Sometimes the mic in doubles as a line in, but most computers have a mic in, headphone out and line in jacks. Audacity's plenty good for the time being. Like you said, you're just dealing with early demos right now.. Audacity not really a serious DAW, but for things like that it works just fine. As to your problem... No idea honestly lol. It could be a few things but it's hard to tell for sure. Maybe try a different cable or adapter?