Hard to say without more info.

White smoke indicates coolant leak (head gasket, etc)
Blue smoke indicates oil leak (rings, etc)

Could also be an external oil leak, oil onto the exhaust for example.

You mention that there was oil on the ground, looking like the coolant had all leaked out. So which was it, oil or coolant?

Could be anything at this point, based on the info provided.

Good luck in any case.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue