Fusion core locations

Total nuclear blocks ------> 73. Locations ------> 21. By location:

Lexington

Mystic Pines Retirement Home in Lexington, in the basement (extended castle)
Find 3 cores on top of the freeway southeast of Sunshine Tidings Co-op , about 3 km west of Lexington, guarded by three demolition men.
The T-51 Power Armor suit is locked in a protective enclosure 50 meters north of Wattz Consumer Electronics (1 km southeast of Lexington). Access to the suit requires hacking a computer terminal (advanced).
In a T-45 power armor suit, locked in a security warehouse on a train car, 1 km west of the Super Duper Mart in Lexington (requires hacking first)

Cambridge

In a T-45 power armor suit at the top of the highway, in the northwest part of the Cambridge police station. Use the yellow elevator up.
Cambridge Police Department , in the garage (motor pool), will find 4 cannonballs in ammunition
In the Director's Room (the key held by Molly is unlocked), at Cambridge Polymer Labs , Cambridge
On a table on the top floor of a building as you enter Cambridge from the north. The building is the one that forms a path above the street on the right.

Arcjet Station

Arcjet Station, find four nuclear cores under the ramp built on the east side of the building. Look for an ammo crate under the shelf.
Arcjet Station, in a room off the lower (smaller) control room with a computer terminal used for rocket engine fire testing
At the electrical substation north of Arcjet Station

Diamond City

Buy 2 Cores from Mirna at the Diamond City Market
Buy 5 Cores from Arturo at the Diamond City Market
Buy 2 Cores from Percy (Mr. Handy) at Myrna's House in Diamond City Market
In the front laundry room of the Layton Towers Hotel , in the Back Bay region, east of Diamond City.
Buy 5 Fusion Cores from Cricket , the vendor outside the Diamond City gates.
Behind the Roadside Pines Hotel , south of Poseidon Reservoir, three kilometers from Diamond City
In the underground tunnel of Bobbi No-Nose in the secure room of Diamond City during the quest "The Big Dig"
The final section of Bobbi No-Nose's tunnel in the Diamond City secure room requires the Expert hacking skill.
In the first room on the left in Wilson Atomatoys Corporate HQ , almost 1 km east of the Diamond City gate.

Fort Hagen

Collect 4 cores from inside the security room on the top floor of Fort Hagen, requiring the Computer Hacking (Advanced) skill.
On the lower level of the generator room of the Fort Hagen Command Center
Another 4 cannonballs can be crafted from ammo in the workshop next to the lower generator room of Fort Hagen.

The Prydwen airship

Good neighborhood

Collect 2 Fusion cells from Hancock's utility room during the quest "The Big Dig" if you decide to fight Bobbi No-Nose.
In the X-01 Mk III Power Armor suit on the roof of 35 Court , near Goodneighbor
Behind the barricade in front of the Mass Fusion building , on the northwest side of Good Neighbor

Gunners Plaza

Glowing Sea

In the X-01 power armor suit in the K-21B installation, Abandoned Shack , in the Glowing Sea.
On the roof of the Atlantic Offices, in the Luminous Sea.
In the cave - "junk cave" 1 km east of the Atom Crater in the Glowing Sea

Mystic Pines

In a suit of T-45 power armor, submerged in a lake east of Mystic Pines, near the plane crash
In the tunnel to the secret compound under Mystic Pines during the quest "Human Error"

Other locations

In the basement of the Longneck Lukovsky Cannery (guarded by hordes of ghouls)
In power armor at the National Guard Training Yard military checkpoint in the northeast.
In the generator room on the roof of Fallon's Department Store
4 Fusion Cores again in the Horror House garage west of Milton Hospital (activate the flamethrower trap outside the cell, then open the door on the left)
Retrieve 2 cores from the basement security enclosure at Greentech Genetics (requires Master hacking skill)
At the southern end of the El-train, accessible from Garden Terrace
In a T-51 Power Armor suit at a military checkpoint 500 meters southwest of Forest Grove Marsh , 1 km southwest of Weston Water Treatment Plant
In a storage room in the western section of the Mass Pike Tunnel West
In a trash can on the north side of Mass Bay Medical Center
In the underground tunnel during the Tradecraft quest, south of the large room with the American flags

Near the end of the underground tunnel for the "Tradecraft" quest, in a small locked box (Novice)
Collect 2 cores from the Sentry Bot in Hesters Consumer Robotics ; after you kill it, of course.
Another 4 Fusion cells in Federal Supply Cache 84NE require Expert Hacking skill.
In a sewer pipe north of Tuffington Boat Yard
Inside Recon Bunker Theta , which you can access during the quest "Lost Patrol",
At the Department of Supply at Boston Airport , southeast of the heavily guarded main entrance
Concord , Freedom Museum Basement (Advanced or Beginner)
Robot Disposal Grounds , in a green military crate next to a sentry bot
USAF Satellite Station Olivia , in a large underground control room

Best