Apparently, in the first edition of Dungeons and Dragons, the following were true:
Black puddings are cold-immune, but can be killed with fire.
Attacks with lightning or regular weapons spread the black pudding into smaller black puddings.
Black puddings corrode metal and dissolve wood.
Black puddings can use ceilings as if they were floors.
Gray Oozes are cold-immune and fire-immune.
Attacks with lightning or regular weapons are the only way to harm Gray Oozes.
Gray Oozes corrode metal and have no effect on wood.
Gelatinous Cubes are cold-immune, but can be killed with fire.
Gelatinous Cubes are lightning-immune but can be killed with regular weapons.
Gelatinous Cubes digest flesh, but not objects.
Gelatinous Cubes stick to floors, ceilings, and walls.
My WMG: Gray Ooze + Black Pudding = Gelatinous Cube.
Gelatinous Cube gets its lightning immunity and fire-vulnerability from Black Pudding.
Gelatinous Cube gets its not-dissolving-wood and vulnerable-to-weapons traits from Gray Ooze, but on the flip side, being able to absorb/be-damaged-by rather than be-spread-into-smaller-ones-of-yourself-by weapons probably also comes from Gray Ooze.
Gray Ooze, Black Pudding, and Gelatinous Cube are all cold-immune, while Ochre Jelly and Green Slime are not (Ochre Jelly and Green Slime are fire-vulnerable, cold-vulnerable, destroy both wood and metal, and cannot be killed with regular weapons or lightning).
Further WMG: If the result of Gray Ooze + Black Pudding was a metal-corroding, weapon-immune, fire-immune monster instead of Gelatinous Cube, it would be a very effective anti-dragon weapon, not only immune to fire and perhaps also claws and stuff (assuming those count as weapons), but corroding and tarnishing their hoards!