Yes, it is possible to grow your money, but you won't be able to grow it rapidly easily (many sites provide scams promising to double or triple your money). You will want a decent amount to start (you won't get anywhere with mere satoshis), and invest in legitimate enterprises, such as known companies, or on reliable and known exchanges.
Even then, there is a risk of loss. Exercise due diligence, and remember that scammers abound. Cloud mining is especially shady with all the ponzis around. See my signature for a resource on some trustworthy and untrustworthy cloud mining providers.