The idea that most world cultures historically performed burial seems quite inaccurate. To take an example, while the Greeks performed burial, the Romans would have mixed traditions : in the earliest remains of Roman funerals, some would bury their dead and some would cremate (and keep ashes and remains in small clay huts typical of the villanovian/early etruscan culture or in biconical urns. Livy has examples that the cremation/inhumation distinction was maintained between the different patrician families in the Early Republican era), which is an interesting token of the fact that the Roman culture was at first probably some sort of composition between differing cultural influences. In any case, by the later Republic and early principate, cremation had become the main type of disposal^1, before a come-back of inhumation, possibly associated to the growing concern for the afterlife associated with eastern cults (Isis worship, early christianity, etc.) around the IIIrd century (cremation would only disappear somewhere in the Vth century as Christianity considers inhumation necessary , in relation with the concept of resurrection of flesh, and the Genesis saying " Memento, homo, quia pulvis es, et in pulverem reverteris "). Ancient Greece also practiced both cremation and inhumation^2, inhumation remaining somewhat more common, possibly due to the cost of wood. As described extensively in the Iliad, Patrocles is supposed to be cremated (in book XXIII, Achilles has to plead with the Gods for favourable winds for the pyre, Hector is also cremated).
Do also keep in mind that Asian cultures outside the Indian subcontinent or its influence (via Buddhist teachings) practice cremation. It is true that Han Chinese would reprieve cremation as unfilial (and unconfucean) but Manchu / Jurchen cremated (before gradually moving to burial under Han influence^3)
^1 : Catullus famously wrote of his brothers ashes (Catullus, Carmen 101)
^2 : Xavier de Schutter, « Rituel funéraire et coût des obsèques en Grèce classique », Kernos, 1989, p. 56
^3 : Elliott, Mark C. (2001). The Manchu Way: The Eight Banners and Ethnic Identity in Late Imperial China, Stanford University Press. p. 264.