Are there innate differences between men's and women's behavior?
This is still a matter of fierce debate between the essentialist and cultural camps.

There is little argument that gender differences are shaped by culture, but there is now a growing evidence supporting the hypothesis that gender differences are also partly the outcome of biological disposition.

Much of such biological disposition is the outcome of hormonal influence. Given that such influence was demonstrated even if prenatal, and that the instructions to the postnatal generation of hormones is coded in our DNA, you can argue that such influence falls into the definition of innate.

You may wish to start with these papers:


Alexander, Gerianne M., and Melissa Hines. "Sex differences in response to children's toys in nonhuman primates (Cercopithecus aethiops sabaeus)." Evolution and Human Behavior 23.6 (2002): 467-479.
Hassett, Janice M., Erin R. Siebert, and Kim Wallen. "Sex differences in rhesus monkey toy preferences parallel those of children." Hormones and behavior 54.3 (2008): 359-364.
Maestripieri, Dario, and Suzanne Pelka. "Sex differences in interest in infants across the lifespan." Human Nature 13.3 (2002): 327-344.