Finlay Butler, eight, and his younger brother Samuel, six, died alongside their cousin Thomas Stewart, 11, and Jack Johnson, 10, in what has been described as a “devastating tragedy”.
Police said no-one witnessed Samuel fall in the water, but “the assumption is that he had rushed towards the danger to help”.
Witnesses described seeing the boys in the water screaming for help before they went under the surface during sub-zero temperatures.
Emergency services rushed to the scene at 2pm and police officers ignored safety advice to form a human chain and wade into the lake in a bid to rescue the boys.
Police used their hands to smash through the ice but were unable to find the boys for another 22 minutes until Jack, Tom and Sam were discovered underwater.
Finlay was recovered from the lake at around 3.05pm having been in the water for 32 minutes but nothing could be done to save the boys.
The hearing was told all four boys had drowned.
Detective chief inspector James Edmonds, of West Midlands Police, told the inquest: “They’d gone to play on the ice.
“For reasons unbeknown, the ice has broken away. It has become fragmented and that has resulted in the boys falling through the ice and into the freezing cold water.
“The impacts of the water temperature would have significantly contributed to the boys being unable to stay afloat.
“It’s a terrible tragedy, my heart and condolences goes out to the families..”
Meanwhile, area commander Alex Shapland, of West Midlands Fire Service, said crews did all they could to rescue the boys who would have gone into shock.
He said: “We have a number of different water capabilities to affect water rescues.
“The water was extremely cold. When you enter water of that temperature your body goes into shock where it makes it very difficult to function.
“We could not have done any more in the time we had.”
Addressing the boy’s families, Birmingham coroner Louise Hunt described the deaths as a “devastating tragedy”.