IN CLUSTER COMPUTING, IS THE AMOUNT OF CORE THAT COUNTS?

no.  it's the application that counts.

If I build a cluster with 8 motherboards with 1 single core each would it
be the same as using just one motherboard but with two quad core
processors?

of course not.  communication among cores on a single board
will certainly be faster than inter-board communication. it's the application that matters: how frequently do threads/ranks of the application communicate? are messages small or large? can the app's communication be formulated as mostly-read sharing of data? these are all very much properties of the application, and they determine how suitable any particular hardware will be.

I wanna build one of these but wanna save money and space and
if what counts is the amount of cores to process info I think fewer
motherboards with dual six-core processors is definitely cheaper just
because I wont be needing that many mothers power supplies etc. thanks

power supplies aren't your main concern, since good ones are about 93%
efficient.  but going with more-core systems is, in general, a good idea.
mainly for amortization reasons: probably fewer disks, extraneous sutff
like video interfaces, fewer parts to fail, fewer systems to administer, etc.
there can be disadvantages to more-core systems too, since some of the parts
being shared (amortized) may be performance bottlenecks.

the sweet spots depends on what systems are in volume production - right now, 2-socket systems are the right building block in most cases. 4-socket systems would be attractive, but they tend to ship in so much lower volume that their price is nonlinearly high. 1-socket servers tend to cost more than half a 2-socket (where "server" means at least "has ECC memory" - that is, not a desktop.)
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