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Pretty sure, even on a Saturday, you'll be on one of the standard, commuter-type trains from Kings Cross (final destination Kings Lynn/Ely? - so you'll be on part of my old commute).
The trains don't have designated bike space. But it'll be fine, as even non-folding bikes are unrestricted at weekends. @pdlouche has some good advice, if the train has the folding-type seats. But a bike will fit in the spaces near the doors no problem. So maybe take a bungee or two / cable to secure it to stop it falling over and sit right next to it, just in case.
Hope you enjoy Cambridge - I might even be there myself with mini c00ps, if the weather's nice tomorrow!
Does anyone know about taking a bike on the train to Cambridge from London? I'm travelling at 8pm on Saturday evening - just tried booking a space but to no avail... Can I just rock up with my bike or are they very militant?