I would call a cluster with 32 nodes and 8 cores in each node a 32 node, 256 CPU cluster.

yes, definitely.  node implies a boundary of memory addressing: after all,
it's a cluster because we need to use distributed-memory programming techniques like MPI to harness it. often nodes that have more cores are called "fat nodes".

I am kinda confused with term cluster and now am sure if this where I can
post my question. What exactly can be defined as a cluster ?, We have a 32
node cluster in our lab. and the number 32 here is referred to 32 separate
machines ( each with its own processor ). What about the new machines
like,
dual core processors or the quad core processors, are those considered
clusters also. For example, should we refer to a quad core processor as a
cluster of 4 processors. Hope someone out there could explain. Thanks
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