If you cast Cull the Weak does that trigger Deflect?

No, casting Cull the Weak does not trigger Deflect.

According to the official rulings for this interaction:

• Deflect only activates when a spell or ability specifically targets (chooses) the permanent with Deflect (Rule 735.1.c).
• Cull the Weak does not target. The choice of which unit to kill happens during the resolution of the spell, not when it is played. Because no targeting occurs, Deflect does not trigger.