We don't know for sure that Dumbledore brought the Elder Wand to the cave. He could have just as easily brought the wand that chose him as an 11-year-old instead of the one he won in a duel. In fact, I don't remember where, but I'm pretty sure I read somewhere that Dumbledore regularly used his other wand, not the Elder Wand...

@Voldemort'sWrath We do know he took it with him, because it's the wand Draco disarms from him (that's the setup for the whole "who controls the wand" thing). They run into Draco right after returning from the cave, so Dumbledore didn't have time to retrieve the Elder Wand from anywhere. (Though I will grant it's been a while since I read the book, so my recollection could be a bit off.)

@Bloodgain - Nope! Actually, the wand that Draco got from Dumbledore was not the Elder Wand! The owner just has to be defeated, and we know that Dumbledore was entombed with the Elder Wand, so it belonged to Draco, even though he never possessed it. Therefore, Dumbledore did not have the Elder Wand with him on the night that he died...

@Voldemort'sWrath I thought it was, Draco disarms Dumbledore, and hence gets ownership of the Elderwand. Harry later disarms Draco and gets ownership of the ElderWand. Snape killed Dumbledore, which made Voldemort believe that he was the Owner of the ElderWand. So Voldemort believed by killing Dumbledore, the ownership of the want would transfer over to him.

@Voldemort'sWrath I do not have the book to hand, but does Draco actually take Dumbledore's wand with him? Or disarm him and leave it lying where it lands? (Of course, since Draco wasn't actually in possession of the Elder Wand when Harry 'defeats' him, we know that Dumbledore doesn't have to have been using the Elder Wand when disarmed)

@Chronocidal - It doesn't matter whether Draco takes it or not...

@Voldemort'sWrath Then what did you mean by "the wand that Draco got from Dumbledore was not the Elder Wand!"? By defeating Draco, Harry claimed mastery of the Elder Wand, which was physically elsewhere. Since you claim the 'evidence' for the wand Draco gets not being the Elder Wand is Dumbledore being entombed with his wand, then whether Draco takes the wand or not does matter.

@Chronocidal Draco didn't physically receive the Elder Wand... He just received its ownership...

@Chronocidal I meant whether he took Dumbledore's regular-use wand, not the Elder Wand because we know that Dumbledore didn't have the Elder Wand with him. Actually, there's a passage from when Harry and Voldemort are about to duel in book 7 where Harry says that Draco never held the Elder Wand; meaning that wasn't the wand he got from Dumbledore...

@Voldemort'sWrath "The door burst open and somebody erupted through it and shouted: 'Expelliarmus!' [...] Then, by the light of the Mark, he saw Dumbledore's wand flying in an arc over the edge of the ramparts and understood ..." (HBP "The Lightning Struck Tower", pg545) So - the Disarming charm is not a Summoning charm, and Draco never held the wand Dumbledore was using on the Astronomy tower. Which may-or-may-not have been the Elder Wand

@Chronocidal Actually, we know for sure that that wasn't the Elder Wand... Here's the passage from Harry Potter: "'The Elder Wand recognized a new master before Dumbledore died, someone who never even laid a hand on it. The new master removed the wand from Dumbledore against his will, never realizing exactly what he had done, or that the world’s most dangerous wand had given him its allegiance. . . .'"

And a sentence later: "'“The true master of the Elder Wand was Draco Malfoy.'"

@Voldemort'sWrath And the disarming spell disarms Dumbledore. The wand flies over the ramparts. Draco never touches it. The disarming spell is not also a summoning spell that brings the wand to your hand - it just knocks it out of your opponent's