I will be in Shanghai for 3 days and then in Beijing for 3 days.

You can purchase the Shanghai Three-day Travel Pass. It is sold CNY45 and could be purchased at any ticket booths set at these subway stations. With this pass, passenger could take all the subway lines without limit in 72 hours after the first use. This pass is not required to be returned after use so passenger could keep it as a souvenir.
However, there is no such 3 days metro pass in Beijing. You are advised to purchase the Ordinary Transportation Card when you arriving there.