The Wikipedia page quotes one Director of DARPA (Stephen J. Lukasik):
The goal was to exploit new computer technologies to meet the needs of military command and control against nuclear threats, achieve survivable control of US nuclear forces, and improve military tactical and management decision making.
And Vint Cerf is quoted elsewhere [1] saying:
the original ARPAnet project was built to share computing resources among all the computer science departments. It was not built _solely_ to deal with nuclear attack, so it was a resource-sharing system