Hack
Join Date: Sep 2015
Location: Ottawa, Ontario, Canada
Posts: 1,265
Bikes: TrueNorth CX bike, 88 Bianchi Strada (currently Sturmey'd), Yess World Cup race BMX, Pure Cruiser race BMX, RSD Mayor v3 Fatbike
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It depends......
Frame may be built for a narrower OLD (wider hub) for the 6 speed, or it may not. Unlike 8-9-10 speed, which are all the same width cassette with narrower gears, 7 speed is very close to the same spacing and wider.
I guess I should specify that I am assuming Shimano components.
If the OLD (outside locknut distance, the distance between the dropouts with the wheel installed) is the same, you should be able to swap to 7 speed very easily.
MTA: The 6 speed is probably a freewheel, not a cassette (threaded interface vs. splined), the 7 speed could be either but likely a freewheel as well.