While your Slingbox has HDMI ports, you would most likely run into HDCP (High Bandwidth Digital Copy Protection) from your cable provider using those. Just a little information on this:
It sounds to me like you already knew this though. To get around this copy protection, you will likely need a way to hook up this HDMI-only cable box to the Slingbox component (red, blue, green, red, white) ports. To do this, we recommend the use of an HDMI adapter. Here is some information on this:
Hope this helps!