In this paper, we derive some new algebraic identities on b 3-subbalancing numbers and obtain the functions that generate b 3-subbalancing numbers. We also introduce b 3-Lucas subbalancing numbers and derive some algebraic identities between b 3-Lucas subbalancing numbers and b 3-subbalancing numbers. Further, we give the Binet formulas for b 3-subbalancing and b 3-Lucas subbalancing numbers.