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Hi this might explain it and help:

Maximum Transmission Unit (MTU)

One setting a router or gateway can influence is the Maximum Transmission Unit (MTU). The MTU determines the largest datagram than can be transmitted by an IP interface (without it needing to be broken down into smaller units). So what does MTU have to do with playing games? Read on…

What does MTU do on Xbox Live?

The MTU of your router or gateway must be greater than or equal to 1365. If it is less than 1365, you won’t be able to connect to Xbox Live.

How do I check my MTU size?

There are two ways. You can check your router or gateway manufacturer’s documentation for your device’s MTU setting. Or, you can let Xbox Live help you. With the latest update of the Xbox Dashboard, you can now determine if your MTU setting is too small for Xbox Live.

To see your MTU setting in the Xbox Dashboard

Select Xbox Live to sign in to XboxLive from the Xbox Dashboard.
From the Connect Status screen, press theY button on your controller.
Press the A button to see diagnostic information. Find MT: x, where xis your MTU test result of either 0 or 1. 0 means your MTU size is not 1365 or greater and it won’t work with Xbox Live. 1 means your MTU size is 1365 or greater and you’re good to go for Xbox Live!
What if my MTU size is not compatible with XboxLive?

If the MT value is 0, you have a router or gateway that is incompatible with Xbox Livebecause ofits MTU setting. You’ll need to change the MTU setting on your device. See your device documentation to accomplish this.

---------- Post added at 09:53 ---------- Previous post was at 09:46 ----------

This applies to both your router and modem if either of them have a MTU value lower than 1365 then you will get this problem so try the test connected directly to each one to determin which one is giving this error. I had the very same problem not long ago and it turned out to be my cable modem which was replaced and now works fine.