Which European coins have a silver outside and a gold center?

Answer 1

None that I know of. The idea behind having a different metal in the core of any coin is to increase the coin's structural integrity. Gold is quite soft and though valuable, would make a poor choice for any coin. You may be thinking of a so-called bimetallic coin. Many countries issue these coins, but they're made of brass and copper-nickel, not gold and silver. Examples are the Canadian $2 coin, the European €1 and €2 coins, and the British £2 coin.

Answer 2

The €2 piece is the most common bimetallic European coin with a silver-colored ring and gold-colored center.

No circulating European Coins contain gold or silver. The silver color is copper-nickel and the gold color is (usually) aluminium brass or a similar alloy.