In the poem "The Soldier," what are the connotations of the phrase "suns of home"?
The "suns of home" can possibly be taken as a homophone for "sons." The soldier who is narrating is fighting in the war (1914-18) alongside other Englishmen, all sons of home, all radiating the hope of going home, of returning victorious at the end of the conflict. To the soldier, it is a blessing, an honor to be in their company—hence the notion that he is "blest by suns of home."
On the other hand, if we look at the definitions of "sun" in the Oxford dictionary, there are two in particular that become relevant and might be a better fit as to connotations. The first is to consider the sun as "a person or thing regarded as a source of glory or inspiration or understanding." The second says the word is "used with reference to someone's success and prosperity." In both cases, we can either apply the notion of the "sons of home" or keep the flow with the previously established theme of England's grandeur.
In the case of the 'sons,' they are proving true and loyal, honorable in every sense—they are glorious, they are an inspiration, and they provide a greater understanding as to the love of one's own country and patriotism. They hopefully will return successful and aid in the prosperity of the soldier's beloved England.
In the case of England's motherly figure and description of magnificence, we can see that she is glorious, that she provides the soldier with the inspiration and understanding to fight. Furthermore, the soldier's sacrifice—as he clearly believes death is imminent (and actually, the author himself, Rupert Brooke, was a soldier in the war and payed the ultimate price) is contributing to England's success. England remains a motherly figure and thus she prospers. She is all that is good and beautiful, all that is abundant and worthy.