Among ethane, ethene, and ethyne the C-C bond energy is

i) A carbon-carbon single bond (Alkanes ) has an average length of 1.54 Angstroms.  
ii) A carbon-carbon double bond (Alkenes) has an average length of 1.33 Angstroms.  
iii) A carbon-carbon triple bond (Alkynes ) has an average length of 1.20 Angstroms. 

Bond length is inversely proportional to the number of bonds between two atoms and bond energy, with increase in the number of bonds between two atoms bond length decreases and bond energy increases. Hence the bond energy of Ethyne is more when compared to ethane and ethene.