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LEASES - Narrative (Details) - USD ($)
$ in Thousands
 3 Months Ended 9 Months Ended
Mar. 31, 2020
Sep. 30, 2019
Mar. 31, 2019
Sep. 30, 2019
Dec. 31, 2019
LEASES          
Lessor, Administrative and late fees income $ 5,400        
Operating Lease, Income, Comprehensive Income [Extensible List]   cube:OtherpropertyRelatedIncomeMember   cube:OtherpropertyRelatedIncomeMember  
Lessee, Operating Lease, Existence of Option to Extend [true false] true        
Lessee, Operating Lease, Existence of Option to Terminate [true false] true        
Right-of-use assets $ 41,532       $ 41,698
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible List] us-gaap:OtherAssetsMember       us-gaap:OtherAssetsMember
Operating lease liabilities $ 46,406       $ 46,391
Operating Lease, Liability, Statement of Financial Position [Extensible List] us-gaap:AccountsPayableAndOtherAccruedLiabilities       us-gaap:AccountsPayableAndOtherAccruedLiabilities
Operating lease weighted-average remaining lease term (in years) 35 years 7 months 6 days       35 years 10 months 24 days
Operating lease weighted-average discount rate 4.74%       4.74%
Operating lease amount paid $ 600   $ 700    
Minimum          
LEASES          
Operating lease term (in years) 1 year        
Operating lease renewal term (in years) 1 year        
Maximum          
LEASES          
Operating lease term (in years) 44 years        
Operating lease renewal term (in years) 69 years