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Artificial molecules are studied using coupled quantum-dot (QD) ensembles with well-defined electronic shells. The coupling strength between the zero-dimensional states is varied by changing the distance between two layers of stacked self-assembled InAs/GaAs QDs. For strongly coupled QDs grown with a 4 nm spacer, state-filling spectroscopy reveals a shift of the QD symmetric state to lower energies by ∼23 meV. The wetting layer states are also strongly coupled because of the shallow confinement, resulting in a redshift of its symmetric state by ∼26 meV.