Ok, there will 1 variable in this calcs.
The variable will be that one time I will use the GBE of the sun asI get it using the formula and one time I will use the one used on wikipedia (which is either more precise or incorrect). (Look here for slightly better explantation why I am uncertain about this one)
Short explanation on frontal area: Just for whoever rechecks this calculations, the frontal area of a planet is calculate as the circle with its radius, so in other words π*r^2. It is not the surface area or half the surface area, because what matters isn't the area of the planet that takes the energy, but the area of the front of the "energy wave / explosion" that hits the planet. Since that is pretty much a wall the area is just a circle. Other physical applications for this can be found for example when calculation and testing air resistance.
Solar System Level
Spherical (omnidirectional) explosion:
Mass Neptune: 1.0243 * 10^26 kg
Diameter Neptune: 49528 km
Radius Neptune: 24764000 m
GBE Neptune: (3*(6.674*10^-11)*(1.0243 * 10^26)^2)/(5*24764000) = 1.6965669512825068648037473752220965918268454207720885155871426264e34 J
Frontal Area Neptune: π*(24764000)^2 = 1.9265995893256955509e15 m^2
Distance Neptune-Sun: 4503443661 km = 4503443661000 m
Area explosion has to cover: 4*π*(4503443661000 m)^2 = 2.5485862284642863478e26 m^2
Energy to destroy Solar System:
(2.5485862284642863478e26 m^2 / 1.9265995893256955509e15 m) * 1.6965669512825068648037473752220965918268454207720885155871426264e34 J
= 2.244289468171002345e45 J
One could consider additional energy for the sun given that one starts the attack at the center, so adding the GBE of the sun on top may be reasonable.
With wikipedias value: 6.87*10^41 + 2.244289468171002345e45 = 2.2449764681710023e45 J
Multi-Solar System Level
With wikipedias GBE
spherical:
Distance to the nearest solar system (proxima centauri) is 4.22 light years = 3.992428e+16 m So with the the radius of the explosion is: 3.992428e+16 m / 2 = 1.996214e16 m
The spherical area it has to cover is: 4*π*r^2
setting in r: 4*π*1.996214e16^2 = 5.0075357464645683119e33 m^2
Frontal area of the sun: π*(696300000m)2 = 1.5231499587168312021e18 m^2
GBE sun: 6.87*10^41 J
Energy to destroy Multi-SS:
(5.0075357464645683119e33 m^2 / 1.5231499587168312021e18 m^2) * 6.87*10^41 J = 2.2585938030155057913e57 J
Galaxy Level
With wikipedias GBE:
Spherical:
Radius Milkyway: 4.7305E+20 m (50000 ly)
Area the explosion has to cover: 4 * π * (4.7305E+20 m)^2 = 2.812055951925949131e42 m^2
Frontal area of sun: π * (696342000 m)^2 = 1.5233337134996349872e18 m^2
Energy to destroy Galaxy:
(2.812055951925949131e42 m^2 / 1.5233337134996349872e18 m^2) * 6.87*10^41 J = 1.2681938447583566593e66 J
Multi-Galaxy Level
With wikipedias GBE:
spherical:
Distance between Major Galaxys: 2.4E+22 m
Radius of the explosion: 1.2e22 m
Surface area sphere: 4*π*r^2
Area explosion has to cover: 1.8095573684677209054e45 m^2
Frontal area of the sun: π*(696300000m)2 = 1.5231499587168312021e18 m^2
Energy to Destroy Multi-Galaxy:
(1.8095573684677209054e45 m^2 / 1.5231499587168312021e18 m^2) * 6.87*10^41 J = 8.1618090525021064444e68 J