Learn Swedish: Får jag smaka på den läckra kakan?

The dictionary form of this adjective is läcker (delicious). In Swedish, adjectives that end in an unstressed -el, -er, or -en drop that 'e' when adding the -a for plural or definite forms. Because of this rule, läcker shrinks to läckra.

Why do we say smaka på instead of just smaka?

When you are actively tasting a specific object (like the cake), you usually use the phrasal verb smaka på. If you just use smaka by itself, it usually describes the flavor something has, like in kakan smakar bra (the cake tastes good).

Why do we use both den and the -n ending on kakan?

This is the Swedish double definite rule. When you put an adjective in front of a specific, definite noun, you need the freestanding article (den for en-words), the definite form of the adjective (läckra), and the noun must still have its definite suffix (kakan).

Does får jag always mean "may I"?