Spring compressed by external constant force,pot.energy stored over it is half of the work done by force, where does half gone

Question

I have a doubt that for an ideal (massless)spring if apply an constant force over it until equilibrium the energy stored over it is ( kx^2)/2 and the work done by force is kx^2 so where the half of the energy gone Also in thermodynamics work done on the gas when a gas is compressed due to a constant pressure over it is Pext(Vf -Vi) irreversibly,why here all the external work is considered Both question are interrelated and contradictory to each other I have an inside feeling that the work in second case should not be be equal to Pext(Vf -Vi) as initially the opposing force is less than that of external one