Right now, No , Cloud Mining is not profitable.

I have invested in a cloud mining site and currently they are not paying me anything as the Bitcoin mined is far less than their mining fee.

There are two major factors involved here. Mining difficulty and Bitcoin price(or the price of the coin your are trying to cloud mine). Most of the cloud mining sites have turned out to be scams. However there are trusted few like Hashflare. Hashflare until yesterday had stopped paying for their SHA 256 Bitcoin mining contracts for nearly a month.
These cloud mining sites have a lot of terms and conditions written in fine line , which you have to consider before signing up or investing .

The problem right now, is the mining difficulty has increased far too much and the price of Bitcoin depreciated periodically to support the level of profitability. Cloud mining sites keep a daily fee which includes the cost of power and infrastructure, hence these costs can't be waived off and are mandatory to be paid by the investor from the daily profits.

It is better to buy coins, and wait for a price hike , rather than mining which has a lot of unpredictable variables involved.