I have a 6W valve guitar amp combo. It has a 8 ohm speaker out. What exactly happens if I connect to a 8 ohm cabinet? What will increase? Volume? Power of course will still be 6W, so what exactly is this for? I play in a very loud band. Mic'in my amp into the PA is not enough, so I was wondering which one would be more effective. Spending money in a more powerful combo (25W? 40W?) or just getting a bigger cabinet.
If you plug in a more sensitive speaker cabinet to the 8 ohm output, then the resulting volume would go up, but because speaker sensitivity is difficult to increase by very much, even the most sensitive speaker you can buy probably won't give you more than a few dB increase in output level.
A few notes about increasing your stage volume: More power helps, but you have to make sure you have a good amount of headroom or else you might get little to no benefit from more power. With an all-tube amp that has adjustable bias, you can sometimes get more headroom by adjusting the bias. A "colder" bias provides more headroom before breakup, and can make the amp sound louder.
If you want to stick with an all-tube combo, you should be fine with 50 Watts of rated power output, as long as the amp isn't biased too hot. 30 to 40 Watts might do also, as long as you have the all the headroom you can get. If you have a 50 Watt amp with good headroom and you still can't hear yourself over the band, IMHO your band is just too darn loud. That's a lot of SPLs.
Regardless of power output and headroom, you can use the tone of the amp to get more (or less) loudness. If you focus the tone on the upper mids and don't try to push too much low end through your combo, you'll get more loudness for the same output level. Remember, loudness is the subjective perception of the intensity, so different frequencies sound louder or softer to human ears even when played at the same sound pressure level. You can take advantage of this by cutting the bass on your amp, using the neck pickup, turning on a "bright" switch if you have it, put the mids, highs, and presence controls all the way up, etc.
One more thing that I like to do with my 50 Watt 1x12" combo that I used to play with in a very loud band is to put it on an amp stand and point it at my ears. That helps me make sure I'm at least able to hear what I'm playing and when you point the amp directly at your head, you'll hear the brightest and frankly most annoying tone that's coming from it. Everyone else who is not directly in line with the amp will hear a more balanced, mellow, and pleasing tone. That means you make sure you can hear yourself well and you're putting the audience's experience first. If your amp is at your knees or ankles pointing straight out, then some poor audience member is getting icepicks in their ears from your amp and you can barely hear it.
A 6W amp won't make a lot of noise no matter how big the cabinet is. To answer part of your question, a cabinet would be louder than, say, a 4" car speaker, but that same cabinet would probably be just as loud as a bigger one. Making noise requires moving air, and moving air takes power, so there are limits on how much air 6W can move. For "very loud", go for a more powerful combo.