Free motorcycle parking Stansted or Luton airport?

Does either Stansted or Luton airport have free motorcycle parking?
I would need to leave my bike from Friday afternoon till Sunday
evening.

Stansted, yes. In the short-stay area just outside the terminal
building. But in the open, so it may get wet.

And its fine to leave a bike there for more than a day?
It won't get detonated by airport security or anything like that?

Again, for Stansted; yes again. I've left mine there for up to a couple
of weeks at the time, without any problems. But it of course depends on
how desirable your bike is, either to steal or as a spares supply.

Last time I was there they had re-done the short stay area, with new
barriers off the road passing by. It was a bit more tricky to get past
the barriers than before, but I did not see any indications that MCs
should pay.

Check the BAA web pages, they might have posted info on MC parking.

I used to leave mine at Luton airport from Friday evening until Sunday
evening with no problems.

I don't know how familiar you are with Luton airport but as you drive
up to the airport there's a roundabout just before the bus drop off
area, on your left as you get to the roundabout is a car park and I
always used that one. There's a nice big railing all the way round and
I used to chain the bike to that with a nice big foad lock to the back
wheel then fit a disc lock to the front wheel to be sure to be sure.

There were always a few locks and chains left attached to the railing
that obviously belonged to regular users who couldn't be arsed to
carry the chain home with them so it must be a popular spot.

Cheers,
Witek

Is that possible ?

Yes.