der Würfel
die
A small, usually six-sided object with numbers or symbols, used in games to produce a random result.
Du bist dran, wirf bitte den Würfel!
It's your turn; please roll the die!

die / cube
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die
A small, usually six-sided object with numbers or symbols, used in games to produce a random result.
Du bist dran, wirf bitte den Würfel!
It's your turn; please roll the die!

The word 'Würfel' (die/cube) is related to the verb 'werfen' (to throw), because a game die is an object that you throw. The verb 'würfeln' (to roll dice/play with dice) is derived directly from the noun.
Wer ist dran mit Würfeln?
Whose turn is it to roll the dice?
The context makes the meaning clear: in connection with games, it refers to the game die. In mathematics, it refers to the geometric shape. In cooking, it means small, cut pieces.
Für das Brettspiel brauchen wir zwei Würfel.
We need two dice for the board game.
The idiom 'Die Würfel sind gefallen' (the die is cast) means that a final decision has been made and can no longer be undone. It is often used in important or dramatic situations.
Nachdem er den Vertrag unterschrieben hatte, wusste er: Die Würfel sind gefallen.
After he had signed the contract, he knew: the die was cast.
In the kitchen, the phrase 'in Würfel schneiden' (to cut into cubes/dice) is often used. In addition, 'Würfel' (cube) is often part of compounds here, such as 'Zuckerwürfel' (sugar cube), 'Speckwürfel' (bacon cubes), or 'Brühwürfel' (bouillon cube).
Für das Gulasch muss man das Fleisch in gleichmäßige Würfel schneiden.
For the goulash, you have to cut the meat into even cubes.
piece
'das Stück' and 'der Würfel' can both refer to a small piece of something, for example with food. 'Stück' is very general: it can have any shape and simply be a part or a single item. 'Würfel' is more precise: it means a small piece in the shape of a cube, that is, with sides of roughly equal length. The words can be confused when something has been cut. If the shape does not matter, you say 'Stück'. If the shape is important, for example with 'Käsewürfel' (cheese cubes) or 'Gemüsewürfel' (vegetable cubes), 'Würfel' is more precise.

Die Lehrerin legt kleine Würfel aus Käse auf den Teller.
The teacher puts small cubes of cheese on the plate.
Adam nimmt in der Pause ein Stück Brot aus seiner Tasche.
During the break, Adam takes a piece of bread out of his bag.