A mixer is the wrong tool for the job if the job is just recording. What you need is a multi-channel audio interface. These have a number of microphone pre-amplifiers, A-D converters and an interface that connects to your computer. You do not give any idea of budget, nor whether you already have any microphones.

Since you will be recording drums, this places additional demands on the choice of both the microphones and the pre-amplifiers because of the large transient characteristics of drum waveforms, and so you should weigh up carefully what to buy.

After you have recorded the individual microphone tracks, you would mix these down to stereo in the computer using a digital audio workstation (DAW) program such as Reaper.

There are hundreds of different microphones and several 8-channel FireWire-interfaced units to choose from. Don't worry if your computer does not have a native FireWire port as plug-in PCI FireWire cards are available relatively cheaply.

Give us an idea of budget and we can come back with some suggestions of what you should be considering, and also what to avoid.

ACtually, he complicated quite what you wanted to know.
IF you just want to record a summing mix of your drums, yes you can conect the mixer straight to the OEM soundcard( most probably through some adapters in order to be compatible with your stereo imput). Now if you want to record them multitracked, then you will need a soundcard interface with as many INS as you might want ( 8 for example is more than enough to get an excelent drum recording). Of course that in this last case you will be limited on how many independent outputs u can have out of temixer( remember that in smaller ones you can use sends as outs, sub groups as outs and panning on the main mix out instead of stereo, so they used as mono( Left 1 right 2, used as mono outs).
So as you see, depends on how good a recording you want .
Hope it helps !!

Soundcards, on the whole SUCK for live music recording (there are some PCI cards out there that are the exception to this, but you didn't stipulate that). Most "OEM" soundcards have terrible mic preamps that were never designed or intended to be used with a low-impedance, balanced microphone, and I've not seen one that had 8 mic inputs as you claimed. As so intelligently explained by Bos, the dynamic range and transients of percussion instruments is such that cheap audio converters overload and smear the signal horribly. The end result will be mush and cheap mixers suffer similar results; when you put the 2 together you get even worse.
BTW, it's iNput, not iMput. Get you act together before coming onto a forum like this and giving "advice".