Battery Power Source for Wireless Router & Modem?
If you want to buy rather than make, consider a UPS:  Battery-backed, automatic battery management, and the AC output can drive any and all wall warts.  You have 64 W of load.  Assume the AC/DC converters you have are 75% efficient.  That raises the total load to 85 W.  Times 8 h equals 680 Wh.  For a 12 V battery device, you need one rated for 57 Ah; 29 Ah for a 24 V battery.