Did you read Bill's scribe that I posted for you
http://www.honda305.com/forums/download.php?id=1489 earlier in this topic? I'd say your carb is shagged. Follow Ed's or Bill's setup advice to the letter: 22.5mm float height
http://www.honda305.com/forums/download.php?id=1494 (measure from the lip, not from the recess indicated by the red line), air screw 1⅛-turns out, needle clip in the middle groove. Start again from there. Clean the plugs,
idle the motor for 5-10 mins with no filter & see what the outcome is with the plugs then.
Then clean the plugs once more and take the bike out for a 15-min ride, avoiding allowing it to idle; inspect the plugs again. If they're still fouling, then I'd say that the needle jet is ovalled or too large.
Also, have you checked the floats for pinholes? If the float isn't floating properly then the fuel level in the bowl will never be correct.
If it still starts
from cold with no choke and runs fine, it's too rich; drop the needle a notch at a time, but bear in mind that the idle jet is what
predominantly sets the mixture at idle. I think I recall that the position of the needle doesn't have overriding control of the fuel/air ratio until around ¼-thottle and above. If the plugs only foul up on idle, turn the air screw
out to weaken the mixture. If they only foul up after a ride, drop the needle a step.
If I was tuning that bike, I'd: clean the carb out with an air nozzle> clean & gap the plugs> check that the floats float> set the float level> start at 1
¼-turns out on the air screw (in view of the fact that it's known to run rich)> run the motor to 'warm', adjust the
idle screw (not the air screw) to attain a fast idle (around 1500rpm) then turn the air screw
in (richer) until the rpm decays; then turn it out (weaker), ¼-turn at a time, until the rpm restores and then starts to falter. Note the ¼-turn (or ⅛-turn for more accurate results) counts between these two points and turn the screw back in by half that count. Clean the plugs again then idle the motor for 5-10 before inspecting the colour once more. If the colour is good (sandy), then ride for a few miles and inspect
yet again to see if the mixture is enriching via the needle jet. It
is long-winded but it's the only way to eventually get it right. You can't short-cut vital adjustments.
Ed should chime in with specifics regarding the single carb motor. I can get a CB running sweet, pretty much, standing on my head, but the C/CA needs somewhat different, if less, attention.