Yea. When your connected to the internet on the Xbox, your game should automatically tell you that you have an update.
Here is how to clear your cache (no internet needed).
Go to the system blade and then select memory.
Press Y on the HD symbol and then press X,X,Left Bumper, Right Bumper, X,X. Once you do this a messsage will appear saying: Do you want to perform maintenance on your Xbox 360 storage devices?
Performing this function will also clear any software updates.