Can sunblock expire?

Possibly. It is a good idea to always follow the expiration dates on medications including skincare. Some active ingredients may breakdown into other/different active molecules over time.
Yes and no. Sunscreen, which is the proper term as no product should be thought of as a sunblock, is an over-the-counter product. As such, you will frequently not find an expiration date on them. I think it is simply a good idea to replace your products every season, just for freshness sake. Any metallic ingredient like titanium or zinc oxide will not expire, but the cream may have ingredients that will.