Not sure about the situation overseas. However, in the US, regardless of whether you receive payment in cash or you provide a receipt, if you have income as is clearly the case here, then you are liable for paying taxes on that income.

There have been a number of high-profile cases here where wealthy/well-known people would pay their nanny's in cash and try to get around employment/tax regulations. When the IRS caught up with them, they had to make amends all around and additionally pay penalties.

Again, just because you don't leave a paper trail does not mean that you aren't liable. Can you get away with not paying the tax - certainly, but if you're caught you are guaranteed that you are going to be paying much more than you owed and additionally have your tax returns scrutinized for a fair amount of time thereafter.