  Triple-W-boson production in proton-proton collisions allows for a direct
access to the triple and quartic gauge couplings and provides a window to the
mechanism of electroweak symmetry breaking. It is an important process to test
the Standard Model (SM) and might be background to physics beyond the SM. We
present a calculation of the next-to-leading order (NLO) electroweak
corrections to the production of WWW final states at proton-proton colliders
with on-shell W bosons and combine the electroweak with the NLO QCD
corrections. We study the impact of the corrections to the integrated cross
sections and to kinematic distributions of the W bosons. The electroweak
corrections are generically of the size of 5-10% for integrated cross sections
and become more pronounced in specific phase-space regions. The real
corrections induced by quark-photon scattering turn out to be as important as
electroweak loops and photon bremsstrahlung corrections, but can be reduced by
phase-space cuts. Considering that prior determinations of the photon parton
distribution function (PDF) involve rather large uncertainties, we compare the
results obtained with different photon PDFs and discuss the corresponding
uncertainties in the NLO predictions. Moreover, we determine the scale and
total PDF uncertainties at the LHC and a possible future 100 TeV pp collider.
