Yes, the hub is identical
Same 5x112 PCD and same 66.6 mm centre bore: wheels from BMW 3 Serie G20-G21 bolt on and centre on Mercedes E-Classe W213 without rings. You still need to check the offset and tyres, detailed below.
≈: width estimated from the original tyre size.
Wheel by wheel: offset and tyres
Each original wheel from BMW 3 Serie G20-G21 is compared with the one from Mercedes E-Classe W213 of the same diameter: how much closer the wheel gets to the shock absorber or how far it sticks out of the wheel arch, and whether the tyre keeps the same overall diameter.
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6.5Jx16 ET22 · 205/60R16 — Check on the car
Compared with the original ≈6.5Jx16 ET32 on Mercedes E-Classe W213: shock absorber side −10 mm, wheel arch side +10 mm, tyre diameter −3 % : fit it with the original tyre size of Mercedes E-Classe W213 (205/65R16), not that of BMW 3 Serie G20-G21.
Comparison for guidance only (estimated width). Check in detail
Before fitting the wheels
An identical hub is not enough: offset, width and diameter change the position of the wheel, and larger calipers can touch a smaller wheel. Original wheels often use bolts or nuts with a specific seat: keep the fixings intended for the wheel, with the thread of Mercedes E-Classe W213 (M14x1.50), tightened to the torque shown on its vehicle page. Finally, check that the size is among the approved fitments for your vehicle. This comparison is for guidance only: have the fitting approved by a professional.
And the other way round: wheels from Mercedes E-Classe W213 on BMW 3 Serie G20-G21?