For this requirement, you would need different cube instances, or archive the data via reports run automatically. As soon as the cube processing finishes successfully, all previous versions of the cube are overwritten.
You could either copy the cube before you process it, e. g. via backup and restore, which can be automated. Or you could archive some reports. E. g. produce some reports from the cube with whichever tool you use for Analysis/Reporting, and archive these.
How many old copies you keep and when you start throwing them away or overwriting is very much dependent on the business requirements. One approach could be to keep the hourly data for 24 hours (i. e. 24 copies), and one daily copy for the last month (i. e. 28 to 31 copies), and after a month to keep only one weekly or one monthly copy.