Are internet speeds divided through router?

I recently purchased a new modem (D-Link CM 500) which supports the speeds from my ISP (TWC). I have the Ultilmate 50 Internet Plan and just recently TWC introduced their Maxxxx internet speeds.  Since they went digital (TV & phone) they were able to free up bandwidth if i understand correctly.  So those who were getting 50 Mbps are now getting 300 Mbps.  So my situation is:  I performed a speed test (three to get an average) on my modem (using my computer) and I am getting 300 Mbps DL and 20Mbps UL. When I connect the modem to the WAN port of my router and run the test the DL speed is more than cut in half (120 Mbps DL and 20 UL). This test was performed with no other devices (wired or wireless) hooked up to the router. The router is a Gigabit router, dual band (ASUS RT AC66U). Before I ran the test I power-cycled the modem and the router and emptied the cache and cleared the cookies from my Mac Book Pro and restarted it, as per the IT tech’s instructions from my ISP. The modem and router are in my IT cabinet and the cable, which I used, was not more than 6 feet long. I chatted with some technicians from my ISP and one of them told me that the bandwidth was being divided to the other devices. I question that answer, because later when I ran the test with only 1 port being used and the others empty (nothing else using or on the wireless portion of the router, there basically wasn’t anything to divide and the speed is more than halved. I don’t want to shell out money on a new router if it’s not the problem. Please someone school me on speeds. By the way, I also went into my router and modems interface to check out the settings. I entered the DL and UL speeds (300 & 20, which my IP supplies) on my QOS page (tab) of my router interface. The firmware on the router and the modem are up to date.  The bottom line or question is “Why is the speed being reduced? I would like to know if my router is bad or if this is normal. Sorry about the information/situation I’m providing is written poorly. Hope you can understand/comprehend my situation. I am appreciative of any feedback. I’m not very tech savvy.