Context. The primary goal of the Kepler mission is the measurement of the frequency of Earth-like planets around Sun-like stars. However, the confirmation of the smallest of Kepler's candidates in long periods around FGK dwarfs is extremely difficult or even beyond the limit of current radial velocity technology. Transit timing variations (TTVs) may offer the possibility for these confirmations of near-resonant multiple systems by the mutual gravitational interaction of the planets. Aims. We previously detected the second planet candidate in the KOI 1574 system. The two candidates have relatively long periods (about 114 d and 191 d) and are in 5:3 resonance. We therefore searched for TTVs in this particularly promising system. Methods. The full Kepler data was detrended with the proven SARS pipeline. The entire data allowed one to search for TTVs of the above signals, and to search for additional transit-like signals.Results. We detected strong anti-correlated TTVs of the 114 d and 191 d signals, dynamically confirming them as members of the same system. Dynamical simulations reproducing the observed TTVs allowed us to also determine the masses of the planets. We found KOI 1574.01 (hereafter Kepler-87 b) to have a radius of 13.49 ± 0.55 R ⊕ and a mass of 324.2 ± 8.8 M ⊕ , and KOI 1574.02 (Kepler-87 c) to have a radius of 6.14 ± 0.29 R ⊕ and a mass of 6.4 ± 0.8 M ⊕ . Both planets have low densities of 0.729 and 0.152 g cm −3 , respectively, which is non-trivial for such cold and old (7−8 Gyr) planets. Specifically, Kepler-87 c is the lowest-density planet in the super-Earth mass range. Both planets are thus particularly amenable to modeling and planetary structure studies, and also present an interesting case where ground-based photometric follow-up of Kepler planets is very desirable. Finally, we also detected two more short-period super-Earth sized (<2 R ⊕ ) planetary candidates in the system, making the relatively high multiplicity of this system notable against the general paucity of multiple systems in the presence of giant planets like Kepler-87 b.