Well you're talking about "good" cadence, what is it? 80? 90?

I have a 10.5 mile commute that used to take around 50-55mins but is now down to 35-45mins. It depends on a whole lot of factors, for instance the difference between the 45 and 35mins is that one way is uphill and the other is downhill. There's also the wind factor, backwind going downhill makes me soar. What also slows your commute are red lights and is the main reason why my commute won't go much faster (other then the fact that I'm moving further from work.. )

Anyway I did shave at least 15 mins since last year and this is due to training and nutrition. I have 32C tires on a cyclocross; do you have drop bars? They will help go faster especially in windy situation.

In terms of nutrition you need to eat correctly, I now always take a recovery drink after my morning commute and eat a banana before. The drink becomes my breakfast, high in carbohydrates and proteins. I also stretch my legs after every ride, stretching greatly reduces leg soreness.

Other then that keep at it, it's not a magic process and it takes time. At the end of the summer you should be much faster. You don't say where you live but if you commute during the winter in snow you'll gain a lot of strength too.