Yes, Cubbit DS3 does have a free tier. You can start for free with 30 GB of storage and 30 GB of download bandwidth for 30 days by signing up here, no credit card required.
After this 30-day trial period (or at any point during the 30-day trial period), you will need to enter a credit card in order to remove the storage and bandwidth restrictions and continue using Cubbit DS3 as a paid subscriber.