It is about 8cm tall and used to be green but is now slowly going white...

Is it some form of tumour?

Edit

Here is the picture of the whole cucumber (for you disbelievers). The growth can be found on the top left and you can find a growing cucumber on the bottom of the same plant:

Split up into the segments, it looks like this:

I have cut up the segments. While cutting, there was a distinct smell of cucumber - the same as when slicing a normal example of the fruit. You can also see some of the wet interior has some shared features with that of a cucumber.

I have also found a hole that could possibly be evidence of an insect being present at some stage of development of this growth, suggesting that Giacomo Catenazzi's answer may be right: