der Kuchen
cake
A sweet baked good made from dough or a mixture and baked in the oven, often with fruit, cream, or chocolate.
Zum Kaffee gibt es heute frischen Apfelkuchen.
Today there is fresh apple cake with coffee.

cake
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cake
A sweet baked good made from dough or a mixture and baked in the oven, often with fruit, cream, or chocolate.
Zum Kaffee gibt es heute frischen Apfelkuchen.
Today there is fresh apple cake with coffee.

Careful: 'Der Kuchen' sounds like the English word 'kitchen', but it means 'cake'. The room where you cook is called 'die Küche' (kitchen) in German. This is a very common mistake.
Meine Oma backt den besten Kuchen der Welt.
My grandma bakes the best cake in the world.
The expression 'Kaffee und Kuchen' (coffee and cake) describes a traditional meal or social gathering in the afternoon in Germany, where people typically drink coffee and eat cake.
Am Sonntag treffen wir uns bei meinen Eltern zu Kaffee und Kuchen.
On Sunday, we're meeting at my parents' place for coffee and cake.
The figurative meaning is usually used in the expression 'ein Stück vom Kuchen abbekommen' (or 'wollen') (to get/want a piece of the cake). This means to receive a share of something valuable, such as money, success, or power.
Bei dem großen Projekt wollen natürlich alle Firmen ein Stück vom Kuchen abbekommen.
Of course, all the companies want to get a piece of the cake in the big project.
cookie / biscuit
'der Kuchen' and 'der Keks' are both sweet baked goods and are often eaten with coffee or tea. The difference is mainly in size, shape, and type. A cake is usually larger, soft or moist, and cut into pieces. A cookie or biscuit is small, flat, and more dry or crispy. Learners may confuse the words because both are baked and sweet. If you cut off a slice, it is usually 'Kuchen'. If you take a small individual baked item from a package, it is usually 'Keks'.

Zum Geburtstag hat Maria einen Schokoladenkuchen gebacken.
Maria baked a chocolate cake for her birthday.
Möchtest du einen Keks zu deinem Tee?
Would you like a cookie with your tea?