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 such 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 are relatively long-period ( about 114d and 191d ) and in 5:3 resonance .
We therefore search for TTVs in this particularly promising system .

Methods : The full Kepler data was detrended with the proven SARS pipeline .
The entire data allowed searching for TTVs of the above signals , as well as searching for additional transit-like signals .

Results : We detect strong anti-correlated TTVs of the 114d and 191d signals , dynamically confirming them as members of the same system .
Dynamical simulations reproducing the observed TTVs allow us to also determine the masses of the planets .
KOI 1574.01 ( hereafter Kepler-87 b ) was found to have a radius of 13.49 \pm 0.55 R _ { \oplus } and a mass of 324.2 \pm 8.8 M _ { \oplus } , and KOI 1574.02 ( Kepler-87 c ) was found to have a radius of 6.14 \pm 0.29 R _ { \oplus } and a mass of 6.4 \pm 0.8 M _ { \oplus } .
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 were ground-based photometric follow-up of K epler planets is very desirable .
Finally , we also detect two more short-period super-Earth sized planetary ( < 2 R _ { \oplus } ) 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 .

Conclusions :