Gaius (born 20 B.C., died 4 A.D.) and his younger brother Lucius were the sons of Augustus' daughter Julia and Marcus Agrippa. Both were adopted by the emperor following the birth of Lucius in 17 B.C., with Gaius the heir apparant. While suppresing the Armenian revolt in 2 A.D., Gaius was wounded during the siege of Artagira. He died 18 months later.
For a similar portrait of Gaius as a boy, compare the example from the Museo Oliveriano, no. 51 in Kleiner, Roman Sculpture.