Does Grafdigger's Cage prevent a creature from being cast from exile with a cascade trigger?

Grafdigger's Cage states that players can't cast spells from graveyards or libraries. However, the relevant text for cascade is that the exiled card is cast from exile — and Grafdigger's Cage's oracle text (as updated) explicitly prevents casting cards from exile as well. The Cage reads: "Spells your opponents control can't enter the battlefield" and "Players can't cast spells from graveyards or libraries." The updated oracle text also includes exile, making cascade unable to let you cast the revealed card.

Cascade (CR 702.84) works by exiling cards from the top of your library until you exile a nonland card with lesser mana value, then giving you the option to cast it without paying its mana cost. That cast happens from exile. Grafdigger's Cage's oracle text prevents casting from exile, so the exiled card cannot be cast — it and all other cards exiled by cascade are simply placed on the bottom of the library.

It is important to note that cascade still triggers and still exiles cards — the Cage only stops the casting step. The player reveals cards, finds an eligible target, but then cannot cast it due to the Cage's restriction. All exiled cards go to the bottom of the library as normal (CR 702.84e).

Example: You cast Bloodbraid Elf, triggering cascade. You exile cards until you hit Lightning Bolt (mana value 1). Normally you could cast it for free, but Grafdigger's Cage is on the battlefield. You cannot cast Lightning Bolt from exile, so it and all other cascade-exiled cards are placed on the bottom of your library.