The author considers finite weighted sums of Kloosterman sums on \(\text{GL}_n\) over the “denominators” and proves a generalization of the famous sum formula of N. V. Kuznetsov [Mat. Sb. 111(153), 334-383 (1980; Zbl 0427.10016)]. One motivation for a formula like this would be to show cancellations in sums of Kloosterman sums in the same way as Kuznetsov did in the classical case, but this would require a nontrivial estimate for the spectral side of the formula.