Can a non-US citizen living in the US on an E2 visa travel to Cuba?

As a person living in the US, you qualify as ‘US Person’, and the travel limitations regarding Cuba apply to you like to any US citizen.
The law requires that you can only travel to Cuba for a defined reason which matches a list of a dozen or so exceptions; as of now, no direct flights are possible without proof of qualification. You can relatively easy qualify for some of these reasons like religious, supporting social development, etc; however, tourism is not on the list. Either of the reasons requires a detailed agenda to be verified, which leaves no time for tourism activity.

Note however that there is no punishment defined in the law, and aside from questioning and getting annoyed, there is theoretically nothing that should happen after violating it - they cannot take your passport, no fee to pay, no jail, etc. For a non-US person, there is the chance that a further Visa application would be denied, but a current cisa should not be affected, as the law does not say so.
I wouldn’t trust that though; that is a high risk to take.

Note also that if you travel through a third country, book the tickets separately, and don’t use your US credit card for it, there is no way for the US authorities to know that you went to Cuba (unless you bring Cuban cigars or other memoribilia...). Example: you book a round-trip to Cayman Islands, Canada, or Mexico, for 8 days; and then book an independant 7-day round-trip from there to Cuba (and not with your US credit card) which fits completely inside the 8 days. This is extensively discussed in internet forums, and often done. You would be violating your patriotic duty, but again, no punishment is defined.