Multiple databases or one large database?
Do the data marts need to have any of different schemas or different backup and recovery strategies? These would justify the separate databases.

Having these data marts has disadvantages:


query performance degradation
logical inconsistency

difficulty to enforce certain constraints between data-marts (unique, FK)
duplication of lookup data in each data mart, followed by drift of values

(globally) inconsistent restores 
operational overhead
HA/DR


Your post does not provide the reasoning why data marts were chosen, so I cannot judge what advantages were leveraged or expected. 

For a more thorough discussion see Multi-Tenant Data Architecture.

If you want performant queries on aggregated data from all data-marts, why not do just that? Aggregate the data-marts into a single DW, powered by columnstores, and enjoy performance.