Does Epic prevent you from casting spells on future turns even if you gained control of new cards?

The Epic ability (CR 702.50) has two components: it copies the spell with the Epic keyword at the beginning of each of your upkeeps for the rest of the game, and — crucially — it states that you can't cast spells for the rest of the game. This restriction is permanent and absolute once the Epic spell resolves.

CR 702.50b specifically reads: 'For the rest of the game, you can't cast spells.' This is a continuous effect with no expiration. It doesn't matter whether you draw new cards, steal cards from opponents, or otherwise gain control of new cards after the Epic spell resolves — none of them can be cast.

The restriction applies to all spell types: creatures, instants, sorceries, enchantments, artifacts, and planeswalkers. You are locked out of casting entirely. You can still play lands, activate abilities, and trigger abilities normally, but casting spells is off the table.

Concrete example: You cast Eternal Dominion (an Epic spell) on your turn. It resolves, and you steal a creature from your opponent. Even though you now control that creature card (say, in a future turn where you might otherwise cast it), you cannot cast it from your hand or anywhere else — the Epic restriction prevents it.

This makes Epic a true double-edged sword: you get a powerful repeating effect every upkeep, but you permanently forfeit the ability to cast any further spells for the rest of the game, no matter what resources you accumulate.