You almost have it, and as @Catija points out additional context is helpful.
I volunteered for (giving) Calculus classes.
I volunteered to give Calculus classes.
has the exact meaning you are looking for.
has the meaning to give up/out something without compensation, to do something willingly.
The prisoner volunteered the information without being tortured.
the prisoner told the information without being tortured
I volunteered Calculus classes.
means "you gave up/out Calculus classes", which doesn't really make sense since a "class" is not something you can "give away", although you can give away "teaching" a class and you can give away your time:
I volunteered my time (to teach a Calculus class).
However, most people will usually understand what you are saying in your first sentence.