Wait, sum of squares of those four numbers?? or whole seven numbers?

Lagrange?

Emirhan wrote: Whenever $3$ odd numbers are given, prove that we can find a fourth odd number such that the sum of squares of all four numbers is a perfect square. \[(2a+1)^2+(2b+1)^2+(2c+1)^2+(2(a^2+b^2+c^2+a+b+c)+1)^2=(2(a^2+b^2+c^2+a+b+c+1))^2.\]