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There's probably more smoke and mirrors involved in that CCA #. The current output capability of a battery cell is determined by its C discharge rate (how much it can dump out the power, like HP output of a motor). Lower quality cells have a low C discharge rate like in the range of 2-10 and are used in less expensive 'deep cycle', backup, trolling motor type batteries. Such a battery if it were an 8Ah battery, with a 10C discharge rate would only discharge at 80A max. You wouldn't find RC hobbyists using such batteries in their toys. Higher performance batteries such as you'd find with A123 cells, or in high performance LG and Samsung cells such as used by Porsche in their battery packs, or in high end cordless tools such as Dewalt or Milwaukee, are capable of a 30C discharge rate. So the same 8Ah battery would be capable of a discharge of 8x30=240A continuous.
However CCA is the measurement of how many amps a 12v lead battery can deliver for 30sec at 0°F while maintaining 7.2v, which for a lead battery is understandable, but for a lithium, how they come up with that number is more of a mystery, the 7.8Ah lithium battery would have to have cells that can discharge at 90C (rare and unlikely) to deliver 700A (7.8*90). Maybe they the cells used have a 45C continuous discharge rate, but might deliver a transient 90C discharge for 2 seconds?
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