What is an example of real application of cubic equations? I didn't yet encounter to a case that need to be solved by cubic equations (degree three) !
May you give me some information about the branches of science or criterion deal with such nature ?

To expand on @DrkVenom's post, elliptic curve cryptography (ECC) is a great example of the deep application of cubics. ECC is currently at the forefront of research in public key cryptography.  It has the important benefit of requiring a smaller key size while maintaining strong security.  Here is an accessible and well-illustrated introduction to the subject:
http://arstechnica.com/security/2013/10/a-relatively-easy-to-understand-primer-on-elliptic-curve-cryptography/
