How to say "I've never done it" without saying what "it" is


I know how to say "I've never done verb-phrase" using verb-phrase ことがない e.g.
ケーキを食べることがない. But how would I say something like

> "Even though I've wanted to try eating cake, **I've never done it** "

Here's my attempt:

> ケーキを食べてみたかったのに、 **そんなことがない**




If you want to say that without repeating yourself or "not saying it" you
could say something like this.

> 今まで食{た}べたいと思{おも}っていたが、まだ口{くち}にしたことがない
>
> I have always wanted to eat cake, but I never have (eaten it).

This last bit infers 「経験{けいけん}」 or experience without actually saying the word
「経験{けいけん}」. ie, 「経験{けいけん}したことがない」

> まだ口{くち}にしたことがない
>
> I have never (eaten)...

Eg,

> 手{て}にしたことがない
>
> This carries the meaning of never getting something.




You can use 経験する for "to experience", and pair it with the grammar point you
mentioned:

I have never experienced (that).

（それを）経験したことがありません

