Context. Main-sequence massive stars embedded in an H ii region should have the same chemical abundances as the surrounding nebular gas+dust. The Cocoon nebula (IC 5146), a close-by Galactic H ii region ionized by a narrow line B0.5 V single star (BD+46 3474), is an ideal target to compare nebular and stellar abundances in detail in the same Galactic region. Aims: We investigate the chemical content of oxygen and other elements in the Cocoon nebula from two different points of view: an empirical analysis of the nebular spectrum, and a detailed spectroscopic analysis of the associated early B-type star using state-of-the-art stellar atmosphere modeling. By comparing the stellar and nebular abundances, we aim to indirectly address the long-standing problem of the discrepancy found between abundances obtained from collisionally excited lines and optical recombination lines in photoionized nebulae. Methods: We collected long-slit spatially resolved spectroscopy of the Cocoon nebula and a high-resolution optical spectrum of the ionizing star. Standard nebular techniques along with updated atomic data were used to compute the physical conditions and gaseous abundances of O, N, and S in eight apertures extracted across a semidiameter of the nebula. We performed a self-consistent spectroscopic abundance analysis of BD+46 3474 based on the atmosphere code FASTWIND to determine the stellar parameters and Si, O, and N abundances. Results: The Cocoon nebula and its ionizing star, located at a distance of 800±80 pc, have a chemical composition very similar to the Orion nebula and other B-type stars in the solar vicinity. This result agrees with the high degree of homogeneity of the present-day composition of the solar neighborhood (up to 1.5 Kpc from the Sun) as derived from the study of the local cold-gas interstellar medium. The comparison of stellar and nebular collisionally excited line abundances in the Cocoon nebula indicates that O and N gas+dust nebular values agree better with stellar values assuming small temperature fluctuations on the order of those found in the Orion nebula (t2 = 0.022). For S, the behaviour is somewhat puzzling, and different conclusions can be reached depending on the atomic data set used. Based on observations made with the William Herschel Telescope operated by the Isaac Newton Group and with the Nordic Optical Telescope, operated by the Nordic Optical Telescope Scientific Association. Both telescopes are at the Observatorio del Roque de los Muchachos, La Palma, Spain, of the Instituto de Astrofísica de Canarias.