The normal process is run the installer (which will fail), allow Oracle as a vendor in the security settings, re-run the VirtualBox installer (which should succeed).
If it doesn't then there may be a permissions issue elsewhere and so can you post the output of running the single command:
ls -laed@ \
/ \
/Applications \
/Applications/VirtualBox.app \
/Applications/VirtualBox.app/Contents/MacOS/VirtualBox \
/Applications/VirtualBox.app/Contents/MacOS/VirtualBoxVM \
/Applications/VirtualBox.app/Contents/MacOS/VBoxRT.dylib \
/Library/Application\ Support/VirtualBox \
/private \
/private/etc \
/private/etc/sudoers \
/private/tmp
-Andy.
My crystal ball is currently broken. If you want assistance you are going to have to give me all of the necessary information.
Please don't ask me to do your homework for you, I have more than enough of my own things to do.