5W40 synthetic is what manufacturer recommends on their new line of BMW's.
This type of oil lasts longer, 10 000 miles, and lubricates better at higher rmp.
Don't change you oil at 3000 miles, it's a waste of money. Synthetic oil does not brake down at 3000 miles or lose any of it's properties. It has same viscosity and maintains it's additives well into 10 000 mile range. Castrol has detailed testing and graphs proving this.
You only change oil often, at 3000 miles, if using conventional oil, which with use and age, loses it's addtitives and viscosity goes up (yes becomes thicher with age thus restricting oil flow, and therefore does not lubricate properly).
Actually it's cheaper to drive on synthetic oil, due to gas savings and much longer oil change intervals, up to 3X longer.
The short answer (for an M54 3.0) is a synthetic oil with an API specification of SH or later. Viscosity of 5W-30 or 5W-40.
the 328i BMW if it is the M52 engine should be using 5w30 synthetic oil, same as the 2.8 Z3
6.9 liters
6.9 quarts
The BMW z4 replaced the BMW z3 in late 2002. The BMW z3 was introduced in 1996 shortly after staring in a James Bond movie. Not as easy on the eyes as the z3 but just as nice.
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7 US quarts
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A BMW X5 and a BMW Z3.