> can't group by that, because I'm trying to get the SUM of the different "duracion"'s of every codasig_cita
Eh? According to you, the result obtained by adding a.hora_cita to the Group By clause is correct.
If there is a real need not to add a.hora_cita to the Group By clause, isolate aggregation in a subquery eg ...
select a.codasig_cita, addtime(a.hora_cita, b.timesum)
from asig_cita2 a
join (
select a.codasig_cita, sec_to_time(sum(time_to_sec(pe.duracion))) as timesum
from asig_cita2 a, citas_proc_empl2 cpe, proc_empl2 pe
where cpe.codproc_empl=pe.codproc_empl and a.codasig_cita=cpe.codasig_cita
group by a.codasig_cita, a.hora_cita
) b using(codasig_cita);
> why in 5.0 throws the correct result?
Probably a bug, see
http://dev.mysql.com/doc/refman/5.6/en/group-by-handling.html.