How can I calculate $gnu(17^3\times 2)=gnu(9826)$ with GAP? I tried to calculate the number of groups of order $17^3\times 2=9826$ with
GAP.
Neither the NrSmallGroups-Command nor the ConstructAllGroups-Command work with GAP. The latter one because of the needed space. Finally, I do not know a formula for $gnu(p^3\times q)$ , with $p,q$ primes and $gnu(n)$=number of groups of order $n$.

Is there any way to calculate such values with GAP ?
Does anyone know a formula for $gnu(p^3\times q)$ for arbitary primes $p,q$ ?

 A: Is there a way to calculate this?
Yes: When one runs larger classification tasks, in particular on parameters that were out of reach when the software was written first time it is not uncommon that some routines get called for input parameters that seemed to be implausible when the code for these routines was written.
Indeed this is what happens here: The calculation gets stuck when calculating the rational classes of a group of order 8192 which has over 2000 conjugacy classes and is represented in a permutation representation of degree over 4000 (though it has a faithful representation of degree 64). While this is a perfectly good group it is far from the examples that were in the code authors mind when writing conjugacy tests. It is not hard to add some basic heuristics that will work around such a situation (I will change this for a future release).
With this the calculation (also for some other orders in the same ballpark) will finish in a few minutes.
If you want, send me (by private mail) a list of orders (excluding multiples of $p^7$) on which the calculation fails and I'll have a look whether similar issues remain.
Oh, and since this is probably the answer you really care about:

 There are 15 groups of order 9826

While there probably is a reasonable description of groups of order $p^3q$, I suspect a formula would end up messy.
