The Shulhan Aruch (Orah Haim 182:1) cites three opinions as to whether there is a requirement to recite Birkat Ha’mazon "Al Ha’kos" – over a cup of wine. This refers to pouring a cup of wine before Birkat Ha’mazon, then reciting Birkat Ha’mazon while holding the cup, and reciting the Beracha of "Ha’gefen" and drinking the wine after Birkat Ha’mazon. The first opinion cited by the Shulhan Aruch is that of the Rambam (Rav Moshe Maimonides, 1135-1204), who maintained that one is never required to recite Birkat Ha’mazon specifically over a cup of wine. The second view, held by several Rishonim, is that one should always recite Birkat Ha’mazon over a cup of wine. The third opinion, that of the Zohar (Parashat Pinhas), is that if three or more men are reciting Birkat Ha’mazon together, with a Zimun, then the leader should recite Birkat Ha’mazon over a cup of wine.
The Shulhan Aruch does not issue a definitive ruling on this issue, but the Ben Ish Hai (Rav Yosef Haim of Baghdad, 1833-1909) and all the scholars of Kabbalah maintained that one should use a cup of wine when a Zimun is made by three or more men. Especially in our time, when wine is readily available and not very expensive, one should make an effort, when possible, to recite Birkat Ha’mazon over a cup of wine when there is a Zimun. Rav Salman Mutzafi (1900-1974) taught that reciting Birkat Ha’mazon over a cup of wine is more valuable than receiving the prestigious Aliya of "Shishi" in the synagogue one thousand times. Using a Kos Shel Beracha (a cup of wine over which Birkat Ha’mazon is recited) has the effect of bringing down great blessings, and so the importance of this practice cannot be overstated.
However, Hacham Bension Abba Shaul (1924-1998) added that Birkat Ha’mazon should not be recited over a cup of wine in the case where two adult males and one minor (below the age of Bar-Misva) recite Birkat Ha’mazon together. Although Sephardic practice follows the opinion that a Zimun is recited in such a case, some Halachic authorities disputed this ruling. Therefore, since the Zohar indicates that a cup of wine should not be used when a Zimun is not recited, it is preferable not to use a cup for Birkat Ha’mazon in a case where one of the three males reciting Birkat Ha’mazon is a minor.
Summary: When three or more men are reciting Birkat Ha’mazon, with a Zimun, Birkat Ha’mazon should be recited over a cup of wine, and there is great spiritual value in doing so. However, if there are only two men over the age of Bar-Misva and one boy under the age of Bar-Misva, then even though a Zimun is recited, a cup of wine should not be used.